Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type

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dc.creatorHeckenberger, I.
dc.date2007-10-24
dc.date2008-10-03
dc.date.accessioned2026-07-07T10:06:56Z
dc.date.available2026-07-07T10:06:56Z
dc.descriptionIn the structure theory of quantized enveloping algebras, the algebra isomorphisms determined by Lusztig led to the first general construction of PBW bases of these algebras. Also, they have important applications to the representation theory of these and related algebras. In the present paper the Drinfel'd double for a class of graded Hopf algebras is investigated. Various quantum algebras, including multiparameter quantizations of semisimple Lie algebras and of Lie superalgebras, are covered by the given definition. For these Drinfel'd doubles Lusztig maps are defined. It is shown that these maps induce isomorphisms between doubles of Nichols algebras of diagonal type. Further, the obtained isomorphisms satisfy Coxeter type relations in a generalized sense. As an application, the Lusztig isomorphisms are used to give a characterization of Nichols algebras of diagonal type with finite arithmetic root system. Key words: Hopf algebra, quantum group, Weyl groupoid
dc.description70 pages
dc.identifierhttps://arxiv.org/abs/0710.4521
dc.identifierhttp://arxiv.org/abs/0710.4521
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170464
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B37; 81R50
dc.titleLusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type
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