A note on symmetric functions in Formanek polynomials
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- by Shmuel Rosset PDF
- Proc. Amer. Math. Soc. 50 (1975), 127-130 Request permission
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.References
- Edward Formanek, Central polynomials for matrix rings, J. Algebra 23 (1972), 129–132. MR 302689, DOI 10.1016/0021-8693(72)90050-6
- S. A. Amitsur, On central division algebras, Israel J. Math. 12 (1972), 408–420. MR 318216, DOI 10.1007/BF02764632
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 127-130
- MSC: Primary 16A38
- DOI: https://doi.org/10.1090/S0002-9939-1975-0366969-4
- MathSciNet review: 0366969