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- W2078468986 abstract "We quantize the generalized-Witt algebra in characteristic 0 with its Lie bialgebra structures discovered by Song–Su [G. Song, Y. Su, Lie bialgebras of generalized-Witt type, arXiv: math.QA/0504168 , Sci. China Ser. A 49 (4) (2006) 533–544]. 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 W ( n ; 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 + n p n in characteristic p . Our results generalize a work of Grunspan [C. Grunspan, Quantizations of the Witt algebra and of simple Lie algebras in characteristic p , J. Algebra 280 (2004) 145–161] 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 [C. Grunspan, Quantizations of the Witt algebra and of simple Lie algebras in characteristic p , J. Algebra 280 (2004) 145–161]) with some techniques from the modular Lie algebra theory." @default.
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- W2078468986 date "2007-06-01" @default.
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- W2078468986 title "Quantizations of generalized-Witt algebra and of Jacobson–Witt algebra in the modular case" @default.
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- W2078468986 doi "https://doi.org/10.1016/j.jalgebra.2007.02.019" @default.
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