TY - JOUR

T1 - A note on symmetric functions in formanek polynomials

AU - Rosset, Shmuel

PY - 1975/7

Y1 - 1975/7

N2 - Formanek's proof of the existence of central identities has the following form: one constructs zz polynomials G(X, Y Y '", ^A, G(X, Y, Y, Y.), etc., whose sum is the desired central identity. The variables X, Y. 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 zz > 2, and connect this question with Amitsur's solution of the general crossed product problem.

AB - Formanek's proof of the existence of central identities has the following form: one constructs zz polynomials G(X, Y Y '", ^A, G(X, Y, Y, Y.), etc., whose sum is the desired central identity. The variables X, Y. 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 zz > 2, and connect this question with Amitsur's solution of the general crossed product problem.

KW - Central identities

KW - Crossed product

KW - Formanek polynomials

KW - Generic matrices

UR - http://www.scopus.com/inward/record.url?scp=84966234468&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1975-0366969-4

DO - 10.1090/S0002-9939-1975-0366969-4

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AN - SCOPUS:84966234468

VL - 50

SP - 127

EP - 130

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -