Pairs of compatible associative algebras, classical Yang-Baxter equation and quiver representations

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dc.creatorOdesskii, Alexander
dc.creatorSokolov, Vladimir
dc.date2006-11-07
dc.date.accessioned2026-07-07T07:32:37Z
dc.date.available2026-07-07T07:32:37Z
dc.descriptionGiven an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such deformations and construct numerous examples. It turns out that these deformations are in one-to-one correspondence with representations of certain algebraic structures, which we call M-structures. We also describe an important class of M-structures related to the affine Dynkin diagrams of A, D, E-type. These M-structures and their representations are described in terms of quiver representations.
dc.description26 pages, latex
dc.identifierhttps://arxiv.org/abs/math/0611200
dc.identifierhttp://arxiv.org/abs/math/0611200
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119172
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B80, 17B63, 32L81, 14H70
dc.titlePairs of compatible associative algebras, classical Yang-Baxter equation and quiver representations
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