A category for the adjoint representation

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dc.creatorHuerfano, Ruth Stella
dc.creatorKhovanov, Mikhail
dc.date2000-02-08
dc.date2001-07-03
dc.date.accessioned2026-07-07T06:26:12Z
dc.date.available2026-07-07T06:26:12Z
dc.descriptionWe construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply-laced quantum group in its adjoint representation. The braid group action in the adjoint representation lifts to an action in the derived category of C. The category C is the direct sum of a semisimple category and the category of modules over a certain algebra A, associated to a Dynkin diagram. In the second half of the paper we show how these algebras appear in the modular representation theory and in the McKay correspondence and explore their relationship with root systems.
dc.descriptionlatex file + 4 eps files with figures; several mistakes found in the original version were corrected, in particular propositions 16-18 required additional assumption of binary G
dc.identifierhttps://arxiv.org/abs/math/0002060
dc.identifierhttp://arxiv.org/abs/math/0002060
dc.identifierJournal of Algebra, 246 (2001), no. 2, 514--542
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97038
dc.subjectQuantum Algebra
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject20G42
dc.titleA category for the adjoint representation
dc.typetext

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