0
$\begingroup$

I have a linear map $T$ on a vector space which satisfies $T^4 = 1$ and want to simplify expressions of the form: $$[X,TY] + [Y,TX] + [Y,T[TX,TY]] + [X,T[TX,TY]],$$ where $[\cdot, \cdot]$ denotes the Lie bracket.

Can Mathematica simplify such expressions? I'm sorry if this is obvious.

Improve this question
$\endgroup$
4
  • $\begingroup$ Did you try to impose the relation as a replacement rule? $\endgroup$
    – user49048
    Commented Jan 4, 2022 at 21:48
  • 1
    $\begingroup$ Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory tour now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. $\endgroup$
    – bbgodfrey
    Commented Jan 4, 2022 at 22:19
  • $\begingroup$ What simplifications do you expect? In your formula there are no terms of $\ge 4$ order in $T$. $\endgroup$
    – yarchik
    Commented Jan 5, 2022 at 8:33
  • $\begingroup$ Yes, it can be done, but you have not provided enough information for us to help you. Please edit your question to improve it. One option, similar to this answer, would be to use the TransformationFunctions options on FullSimplify. $\endgroup$
    – rhermans
    Commented Jan 5, 2022 at 9:21

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.