Consider 3 non-commutative elements $A,B,C$ and we have the relation $CB=\alpha BC$.
I want to compute things like : $(A\otimes BC ) ( B \otimes B) = AB \otimes \alpha B^2C$
Is there any package doing this ?
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Dot for your noncommutative multiplication, we can encode your relation with:
B /: C . B := α B . C
KroneckerProduct for your "⊗" operation, the output you want to get can then be obtained with:
KroneckerProduct[A, B.C].KroneckerProduct[B, B] //TensorExpand
α KroneckerProduct[A.B, B.B.C]