A note on symmetric functions in Formanek polynomials
Abstract: Formanek's proof of the existence of central identities has the following form: one constructs polynomials , etc., whose sum is the desired central identity. The variables are generic matrices. These 's commute pairwise which raises the question whether all symmetric functions in them also give central identities. Here we show that this is not so for , and connect this question with Amitsur's solution of the general crossed product problem.
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Keywords: Formanek polynomials, generic matrices, central identities, crossed product
Article copyright: © Copyright 1975 American Mathematical Society