Calculating in the group ring $Q[GL_n(Z)]$

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I am trying to use Mathematica to check some identities in the group ring $Q[GL_n(Z)]$. Is there a package/function of Mathematica to do this?

Thanks a lot in advance!

Graumagier

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asked Nov 28, 2015 at 12:12

Mike

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$\begingroup$ What identities in particular? $\endgroup$
– Patrick Stevens
Commented Nov 28, 2015 at 12:20
$\begingroup$ Identities of the type in arxiv.org/pdf/1404.5048.pdf Proposition 2.2 on the top of page 6. Not exactly those but mine are of the same "type". $\endgroup$
– Mike
Commented Nov 28, 2015 at 12:37
$\begingroup$ Long time ago I worked on certain polynomial identities algebras and I used Mathematica for experiments and proofs derivations. Since those algebras had representations in the matrix ring I used symbolic matrices replacement rules, and the functions Inner and NonCommutativeMultiply to represent and investigate identities. (See this response for an example.) $\endgroup$
– Anton Antonov
Commented Nov 28, 2015 at 14:54
$\begingroup$ Thanks a lot this was helpfull! $\endgroup$
– Mike
Commented Nov 28, 2015 at 17:21

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