Quantizations of generalized-Witt algebra and of Jacobson-Witt algebra in the modular case

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dc.creatorHu, Naihong
dc.creatorWang, Xiuling
dc.date2006-02-13
dc.date2007-02-11
dc.date.accessioned2026-07-07T08:07:33Z
dc.date.available2026-07-07T08:07:33Z
dc.descriptionWe quantize the generalized-Witt algebra in characteristic 0 with its Lie bialgebra structures discovered by Song-Su (\cite{GY}). Via a modulo p reduction and a modulo "p-restrictedness" reduction process, we get 2^n{-}1 families of truncated p-polynomial noncocommutative deformations of the restricted universal enveloping algebra of the Jacobson-Witt algebra \mathbf{W}(n;\underline{1}) (for the Cartan type simple modular restricted Lie algebra of W type). They are new families of noncommutative and noncocommutative Hopf algebras of dimension p^{1+np^n} in characteristic p. Our results generalize a work of Grunspan (J. Algebra 280 (2004), 145--161, \cite{CG}) in rank n=1 case in characteristic 0. In the modular case, the argument for a refined version follows from the modular reduction approach (different from \cite{CG}) with some techniques from the modular Lie algebra theory.
dc.description24 pages; final revised version. Journal of Algebra (to appear)
dc.identifierhttps://arxiv.org/abs/math/0602281
dc.identifierhttp://arxiv.org/abs/math/0602281
dc.identifierJournal of Algebra 312 (2), (2007), 902--929
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130969
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B37;17B62;17B50
dc.titleQuantizations of generalized-Witt algebra and of Jacobson-Witt algebra in the modular case
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