Modular quantizations of Lie algebras of Cartan type $H$ via Drinfeld Twists
| Autor: | Tong, Zhaojia, Hu, Naihong, Wang, Xiuling |
|---|---|
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Contemp. Math. 652 (2015), 173--205. (A special volume dedicated to Prof. H. Strade) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/conm/652/12980 |
| Popis: | We construct explicit Drinfel'd twists for the generalized Cartan type $H$ Lie algebras in characteristic $0$ and obtain the corresponding quantizations and their integral forms. Via making modular reductions including modulo $p$ reduction and modulo $p$-restrictedness reduction, and base changes, we derive certain modular quantizations of the restricted universal enveloping algebra $\mathbf u(\mathbf{H}(2n;\underline{1}))$ in characteristic $p$. They are new non-pointed Hopf algebras of truncated $p$-polynomial noncommutative and noncocommutative deformation of prime-power dimension $p^{p^{2n}-1}$, which contain the well-known Radford algebras as Hopf subalgebras. As a by-product, we also get some Jordanian quantizations for $\mathfrak {sp}_{2n}$. Comment: 33 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|