A N-extended version of superalgebras in D=3,9 mod 8
A set of generalized superalgebras containing arbitrary tensor p-form operators is considered in dimensions $D=2n+1$ for $n=1,4 mod 4$ and the general conditions for its existence expressed in the form of generalized Jacobi identities is established. These are then solved in a univoque way and some lowest dimensional cases $ D= 3, 9, 11 $ of possible interest are made explicit.