Mariano Suárez-Alvarez

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Name        Mariano Suárez-Alvarez
Member for  3 years
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Location    Buenos Aires
Age         39

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| 57m   | comment  | What is an interpretation of the relation in the cohomology of the pure braid groups?One you notice that those forms are closed (and considering those forms is very natural once you see that you are working with an arrangement of hyperplanes), the relations of Arnold are the very first that come to mind. Why would one conjecture that these are all relations, I don't know, but that these forms generate the whole thing is a sensible optimistic guess —although Arnold surely had reasons too. |
| 1d    | comment  | What is the 31th homotopy group of the 2 - sphere ?«For separable states, the original Hilbert space $S^7$ simplifies to $S^2\times S^2$» Reading physics papers requires a lot of restraint :-)                                                                                                                                                                                                                                                                                                             |
| 1d    | comment  | Reference request: Riemannian manifold of  linear isometries from $\mathbb{C}^n$ into $\mathbb{C}^m$@Tysin, it is clear that your question is not sufficiently transparent as to what exactly it is asking for —maybe elaborating more on what you are looking for will make it easier for you to find it. Your comment here is also rather opaque :-)                                                                                                                                                       |
| 1d    | comment  | What is the 31th homotopy group of the 2 - sphere ?But there is no fourth Hopf fibration!                                                                                                                                                                                                                                                                                                                                                                                                                    |
| 1d    | comment  | What is the 31th homotopy group of the 2 - sphere ?In what way the two things you list as motivation are motivation for asking what the 31st homotopy group is?                                                                                                                                                                                                                                                                                                                                              |
| 2d    | comment  | A catalog of faithful representations of finite groups?There is no need of the «with repetitions» part: the smallest faithful reps are always multiplicity free.                                                                                                                                                                                                                                                                                                                                             |
| May15 | comment  | A catalog of faithful representations of finite groups?At the very least, explain what you mean by noteworthy...                                                                                                                                                                                                                                                                                                                                                                                             |
| May15 | comment  | Special automorphisms of extraspecial groups @John, as soon as you get 50 points of reputation you will be able to add comments. Using the answer box to respond to someone's answer does not work at all.                                                                                                                                                                                                                                                                                                   |
| May14 | comment  | Awfully sophisticated proof for simple facts(You can avoid the strange substraction of two equal numbers in the end by using the reduced Euler characteristic; this is a standard trick) This of course subjective, as it depends on one's background, but this does not seem awfully sophisticated at all to me and, instead, appears quite natural! :-)                                                                                                                                                    |
| May13 | comment  | What is the “fundamental theorem of invariant theory” ?This question reminds me of the Jabberwocky poem :-)                                                                                                                                                                                                                                                                                                                                                                                                  |
| May13 | comment  | Proper actions  on unitary  spheres  of  a  Hilbert  spaceEvery torsion free discrete group $G$ acts properly and discontinuousy on the unit sphere of $L^2(G)$, no?                                                                                                                                                                                                                                                                                                                                         |
| May13 | comment  | Isomorphic maximal commutative semi-simple sub algebras of M_n(C).  Don't ask questions in answer boxes (!) If you want another question, ask a new question.                                                                                                                                                                                                                                                                                                                                                |
| May13 | comment  | If $M_n(R)$ and $M_m(R)$ satisfy the same polynomial identities is it true that $m=n$?@Thiago, I was just providing an example to Pasha's second paragraph, quite independently of what the question asked for.                                                                                                                                                                                                                                                                                              |
| May12 | comment  | Is there an analogue of curvature in algebraic geometry?Well, in order to get an isomorphism, you changed both the domain and the codomain of the map. The original domain and codomains had certain interest of their own, so the fact that after redefining things you do get an isomorphism may be not as useful as it may appear initially when seem from the point of view of the contexts where the question originally arose :-)                                                                      |
| May12 | comment  | Normal regular sequence in noncommutative algebrasIf you explained what is that «some result» in the homogeneous case, it might be easier to see what you are after in the general case.                                                                                                                                                                                                                                                                                                                     |
| May12 | comment  | Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety?Your question specializes to «is there a simple way of writing down the singular cohomology of a hypersurface in $P^n$?» One can compute the dimensions of the rational cohomology groups if the surface is smooth, I think, but I  don't know if the ring structure comes out as easily.                                                                                                                    |
| May12 | comment  | H^d[U(1)^n,U(1)] of the Borel cohomology and Chern-Simons theoryI for one still don't know what cohomology you are talking aboout —Konrad asked you to be specific about this a few weeks ago but you haven't answered that afaict. Without knowing that, it is simply impossible to even make sense of what you are asking! For example, the answer by Henr.L below seems to have decided that you are taking about singular cohomology of the space $U(1)^n$, which I think is quite surely no the case... |
| May11 | comment  | A characterization of Hilbert spaces?Dear Wlodzimierz, you can find formatting tips on this page htpp://mathoverflow.net/editing-help; in particular, a common way to get a link you have to use the syntax [some text](the actual URL). I hope your time on MO is not that bad, because I for one enjoy very much reading your contributions!                                                                                                                                                               |
| May11 | comment  | Resolutions of Lie algebrasCan't you just copy what Tate did? Pick a presentation; start with the free Lie algebra on the generators, add a generators $y$ of degree $1$ per relation $r$, and define $d(y)=r$. Find generators for the homology of this dg, lift them to cycles, add generators to kill them and so on.                                                                                                                                                                                     |
| May11 | comment  | non-convex Polytope definition.There are various definitions of what regularity should mean in Coxeter's book Regular polytopes.                                                                                                                                                                                                                                                                                                                                                                             |
| May11 | comment  | If $M_n(R)$ and $M_m(R)$ satisfy the same polynomial identities is it true that $m=n$?If $R$ is a ring of row-finite column finite infinite matrices, then $R\cong M_2(R)$.                                                                                                                                                                                                                                                                                                                                  |
| May11 | comment  | Awfully sophisticated proof for simple factsThis was popular among whom? The book by Cartan and Eilenberg, the very first textbook on the subject, already has the computation done in terms of the usual very small periodic projective resolution: after that, using anything else to compute this seems pretty weird!                                                                                                                                                                                     |
| May10 | comment  | A characterization of Hilbert spaces?Adding a link to the earlier question (specially if you use the notation introduced there) would be useful.                                                                                                                                                                                                                                                                                                                                                             |
| May10 | comment  | Tenacious structure Notice that if one projectivizes $\mathbb A^d$ (with origin set at $p$) then one knows that the resulting projective space $\mathbb P^{d-1}(\mathbb F_3)$ does have a «cellular decomposition» and the question is asking if one can find one such decomposition which lifts to a decomposition of $X$ —the converse is obvious.                                                                                                                                                         |
| May10 | asked    | Tenacious structure                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
| May10 | comment  | Functional equationsUmar did not say pretty much anything, really!                                                                                                                                                                                                                                                                                                                                                                                                                                           |
| May9  | comment  | Binary Operation on a Cubic Surface(You should get the second edition)                                                                                                                                                                                                                                                                                                                                                                                                                                       |
| May9  | comment  | Binary Operation on a Cubic SurfaceThere is a book by Manin on, more or less, this subject: Cubic forms.                                                                                                                                                                                                                                                                                                                                                                                                     |
| May5  | comment  | What arithmetic information is contained in the algebraic K-theory of the integersBeautiful answer!                                                                                                                                                                                                                                                                                                                                                                                                          |
| May4  | comment  | Can you compute the quotient set below? Your comment makes me think that you misunderstand what I wrote. I did noy say that the two polynomials $X^2$ and $X(X+1)$ are in the same orbit ---I said exactly the opposite. The rest of the comment, I don't understand it.                                                                                                                                                                                                                                     |
| May4  | revised  | Can you compute the quotient set below? added 270 characters in body; added 1 characters in body                                                                                                                                                                                                                                                                                                                                                                                                             |
| May4  | revised  | Can you compute the quotient set below? added 184 characters in body                                                                                                                                                                                                                                                                                                                                                                                                                                         |
| May4  | comment  | Can you compute the quotient set below? I did not say that you would arrive at a different problem: but the version with polynomials is expressed in terms of familiar things —polynomials and linear changes of variables— instead of weird ordered pairs under an unmotivated equivalence relation!                                                                                                                                                                                                        |
| May4  | answered | Can you compute the quotient set below?                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |
| Apr27 | revised  | Quotients of classifying spacesadded 414 characters in body                                                                                                                                                                                                                                                                                                                                                                                                                                                  |
| Apr27 | revised  | Quotients of classifying spacesadded 48 characters in body                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
| Apr27 | answered | Quotients of classifying spaces                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
| Apr23 | asked    | What is flexible about flexible algebras?                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |
| Apr20 | accepted | Associative algebras with Jacobson radical of codimension 1                                                                                                                                                                                                                                                                                                                                                                                                                                                  |
| Apr20 | answered | Associative algebras with Jacobson radical of codimension 1                                                                                                                                                                                                                                                                                                                                                                                                                                                  |
| Apr15 | revised  | The intersection complex and the Cohen-Macaulay propertyedited title                                                                                                                                                                                                                                                                                                                                                                                                                                         |
| Apr14 | revised  | complete or open Kähler  manifold and  simply connected edited body; edited title                                                                                                                                                                                                                                                                                                                                                                                                                            |
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| Mar31 | revised  | The octonions on a bad dayadded 121 characters in body; edited body                                                                                                                                                                                                                                                                                                                                                                                                                                          |
| Mar31 | asked    | The octonions on a bad day                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
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