On a Family of Non-Unitarizable Ribbon Categories

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dc.creatorRowell, Eric C.
dc.date2004-03-12
dc.date2005-03-02
dc.date.accessioned2026-07-07T05:06:21Z
dc.date.available2026-07-07T05:06:21Z
dc.descriptionWe consider two families of categories. The first is the family of semisimple quotients of H. Andersen's tilting module categories for quantum groups of Lie type $B$ specialized at odd roots of unity. The second consists of categories constructed from a particular family of finite-dimensional quotients of the group algebra of Artin's braid group known as $BMW$-algebras of type $BC$. Our main result is to show that these families coincide as braided tensor categories using a recent theorem of Tuba and Wenzl. The morphism spaces in these categories can be equipped with a Hermitian form, and we are able to show that these categories are never unitary, and no braided tensor category sharing the Grothendieck semiring common to these families is unitarizable.
dc.description25 pages, 1 figure. Final verstion to appear in Math. Z. Changes: expanded to include Lie type C, clarified/justified use of fusion rule result due to Andersen-Paradowski and to Sawin in the general case (reference added)
dc.identifierhttps://arxiv.org/abs/math/0403217
dc.identifierhttp://arxiv.org/abs/math/0403217
dc.identifierMath. Z. vol. 250 no. 4 (2005) 745-774.
dc.identifierdoi:10.1007/s00209-005-0773-1
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70442
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject20G42,17B37(Primary);18D10,20F36,20C08(Secondary)
dc.titleOn a Family of Non-Unitarizable Ribbon Categories
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