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

Rings and Algebras;Category Theory