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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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    $\begingroup$ Check the NCAlgebra package (I am not very familiar with it so I can't give an answer, but it's the biggest/oldest package dealing with such problems). $\endgroup$ – Szabolcs Mar 21 at 8:25
  • $\begingroup$ try www.github.com/NCAlgebra/NC $\endgroup$ – Slepecky Mamut Mar 21 at 8:39
  • $\begingroup$ This package deals with non commutative algebra but it doesn't seem to treat tensor products $\endgroup$ – Nico045 Mar 21 at 10:16
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    $\begingroup$ You don't need a package. Just give Mathematica the rules for working with non-commutative multiplication and tensor product. $\endgroup$ – Somos Mar 21 at 14:46
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Using Dot for your noncommutative multiplication, we can encode your relation with:

B /: C . B := α B . C

Using 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]

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