Operations and Identities in Tensor Algebra
  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. 
Yu. Chernyakov, V. Dolotin