Operations and Identities in Tensor Algebra

Abstract

We define the class of non-decomposable $N$-ary operations in the mixed tensor algebra $\underset{i,j=0}{\overset{\infty }{⨁}}{A}_i^j$. There are higher Jacobi-like identities for (binary) deformed matrix commutator and a 3-ary operation which is non-decomposable into binary ones.

12 pages, 8 figures