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 |
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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: | https://eprints.maths.manchester.ac.uk/id/eprint/730 |

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