Algebraic structures connected with pairs of compatible associative algebras

Odesskii, Alexander and Sokolov, Vladimir (2006) Algebraic structures connected with pairs of compatible associative algebras. International Mathematics Research Notices, 2006. pp. 1-35. ISSN 1073-7928

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Abstract

We study associative multiplications in semisimple associative algebras over ℂ compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over ℂ. It turns out that these deformations are in one-to-one correspondence with representations of certain algebraic structures, which we call M-structures in the matrix case and PM-structures in the case of direct sums of several matrix algebras. We also investigate various properties of PM-structures, provide numerous examples and describe an important class of PM-structures. The classification of these PM-structures naturally leads to affine Dynkin diagrams of A,D,E-types.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry
MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras
Depositing User: Ms Lucy van Russelt
Date Deposited: 27 Mar 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/730

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