Algebraic structures connected with pairs of compatible associative algebras

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dc.creatorOdesskii, Alexander
dc.creatorSokolov, Vladimir
dc.date2005-12-21
dc.date2006-02-02
dc.date.accessioned2026-07-07T06:55:38Z
dc.date.available2026-07-07T06:55:38Z
dc.descriptionWe study associative multiplications in semi-simple 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-type.
dc.description29 pages, Latex. The case of semi-simple algebras A and B is completed (Chapter 4). A construction of compatible products is added (Chapter 1)
dc.identifierhttps://arxiv.org/abs/math/0512499
dc.identifierhttp://arxiv.org/abs/math/0512499
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106341
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectRings and Algebras
dc.subjectRepresentation Theory
dc.subjectExactly Solvable and Integrable Systems
dc.subject17B80, 17B63, 32L81, 14H70
dc.titleAlgebraic structures connected with pairs of compatible associative algebras
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