Twists and quantizations of Cartan type $H$ Lie algebras

Details Twists and quantizations of Cartan type $H$ Lie algebras Twists and quantizations of Cartan type $H$ Lie algebras

2012-02-26

arxiv.org/abs/1202.5730v1

Mathematics

Quantum Algebra

24 pages. arXiv admin note: text overlap with arXiv:0902.2821

Scientific paper

We construct explicit Drinfel'd twists for the generalized Cartan type $H$ Lie algebras and obtain the corresponding quantizations. By modular reduction and base changes, we obtain certain modular quantizations of the restricted universal enveloping algebra $\mathbf u(\mathbf{H}(n;\underline{1}))$ in characteristic $p$. They are new Hopf algebras of truncated $p$-polynomial noncommutative and noncocommutative deformation of prime-power dimension $p^{p^{2n}-1}$, which contain the well-known Radford algebra as a Hopf subalgebra. As a by-product, we also get some Jordanian quantizations for $\mathfrak {sp}_{2n}$.

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