Algebras with polynomial identities and Bergman polynomials. (English) Zbl 1119.15016

Rashkova, Tsetska G.

Mladenov, Ivaïlo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9–14, 2006. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-37-0/pbk). 292-301 (2007).

Summary: This paper is an introduction to the theory of algebras with polynomial identities. It stresses on matrix algebras and polynomial identities for them. The notion of Bergman polynomials is introduced. Such types of polynomials are investigated being identities for algebras with symplectic involution. In the Lie case more information is given for Bergman polynomials as Lie identities for the considered algebras.
For the entire collection see [Zbl 1108.53003].

MSC:

15A30	Algebraic systems of matrices
16R10	\(T\)-ideals, identities, varieties of associative rings and algebras
16R30	Trace rings and invariant theory (associative rings and algebras)
16R50	Other kinds of identities (generalized polynomial, rational, involution)

Keywords:

algebras with polynomial identities; matrix algebras; polynomial identities; Bergman polynomials; symplectic involution; Lie identities