A generalization of Coxeter groups, root systems, and Matsumoto's theorem

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dc.creatorHeckenberger, I.
dc.creatorYamane, H.
dc.date2006-10-27
dc.date.accessioned2026-07-07T07:29:30Z
dc.date.available2026-07-07T07:29:30Z
dc.descriptionThe root systems appearing in the theory of Lie superalgebras and Nichols algebras admit a large symmetry extending properly the one coming from the Weyl group. Based on this observation we set up a general framework in which the symmetry object is a groupoid. We prove that in our context the groupoid is generated by reflections and Coxeter relations. This answers a question of Serganova. Our weak version of the exchange condition allows us to prove Matsumoto's theorem. Therefore the word problem is solved for the groupoid.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/0610823
dc.identifierhttp://arxiv.org/abs/math/0610823
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/118136
dc.subjectQuantum Algebra
dc.subjectGroup Theory
dc.subject20M05; 20F55; 17B20
dc.titleA generalization of Coxeter groups, root systems, and Matsumoto's theorem
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