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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on symmetric functions in Formanek polynomials

Author: Shmuel Rosset
Journal: Proc. Amer. Math. Soc. 50 (1975), 127-130
MSC: Primary 16A38
MathSciNet review: 0366969
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Abstract: Formanek's proof of the existence of central identities has the following form: one constructs $ n$ polynomials $ G(X,{Y_1},{Y_2}, \cdots ,{Y_n}),G(X,{Y_2}, \cdots ,{Y_n},{Y_1})$, etc., whose sum is the desired central identity. The variables $ X,{Y_i}$ are generic matrices. These $ G$'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 $ n > 2$, 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

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