Quantizations of generalized-Witt algebra and of Jacobson–Witt algebra in the modular case
Abstrak
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.
Topik & Kata Kunci
Penulis (2)
N. Hu
Xiuling Wang
Akses Cepat
- Tahun Terbit
- 2006
- Bahasa
- en
- Total Sitasi
- 37×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1016/J.JALGEBRA.2007.02.019
- Akses
- Open Access ✓