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Zbl 1119.15016
Rashkova, Tsetska G.
Algebras with polynomial identities and Bergman polynomials. (English)
[A] Mladenov, Iva\"ilo (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. 292-301 (2007). ISBN 978-954-8495-37-0/pbk

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.

MSC 2000:: *15A30 Algebraic systems of matrices
16R10 Varieties of rings and algebras
16R30 Trace rings and invariant theory (assoc. rings and algebras)
16R50 Other kinds of identities of assoc. rings

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

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