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Title: Algebras, Dialgebras, and Polynomial Identities
Authors: R. Bremner, Murray
Keywords: Algebras
Triple Systems
Triple Disystems
Polynomial Identities
Multilinear Operations
Computer Algebra
Issue Date: 2012
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 38, No 1-3, (2012), 91p-136p
Abstract: 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 Raúl Felipe, Luiz A. Peresi, and Juana Sánchez-Ortega.
Description: 2010 Mathematics Subject Classification: Primary 17A30. Secondary 16R10, 17-08, 17A32,
ISSN: 1310-6600
Appears in Collections:Volume 38, Number 1-3

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