A note on symmetric functions in formanek polynomials

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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.

Original languageEnglish
Pages (from-to)127-130
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Jul 1975


  • Central identities
  • Crossed product
  • Formanek polynomials
  • Generic matrices


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