Algebras, dialgebras, and polynomial identities

Details Algebras, dialgebras, and polynomial identities Algebras, dialgebras, and polynomial identities

2012-01-16

arxiv.org/abs/1201.3379v1

Mathematics

Rings and Algebras

32 pages

Scientific paper

This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting operations in algebras into operations in dialgebras; Lie and Jordan triple systems, and the corresponding disystems; and a noncommutative version of Lie triple systems based on the trilinear operation abc-bca. The paper concludes with a conjecture relating the KP and BSO algorithms, and some suggestions for further research. Most of the original results are joint work with Raul Felipe, Luiz A. Peresi, and Juana Sanchez-Ortega.

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