Algebras with polynomial identities and Bergman polynomials.

*(English)* Zbl 1119.15016
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.

##### MSC:

15A30 | Algebraic systems of matrices |

16R10 | $T$-ideals, identities, varieties of rings and algebras |

16R30 | Trace rings and invariant theory (associative rings and algebras) |

16R50 | Other kinds of identities of associative rings |