2014/10/31 by Zhaojia Tong, Naihong Hu
Mathematics · #math.QA
paper · pdf · doi:10.1016/j.jalgebra.2015.10.016
published as J. Algebra 450 (2016), 102--151 · arXiv admin note: substantial text overlap with arXiv:1202.5730, arXiv:0902.2821
arxiv created 2015/12/20 · arxiv updated 2015/12/22
We construct explicit Drinfel'd twists of Jordanian type for the generalized Cartan type K Lie algebras in characteristic 0 and obtain the corresponding quantizations, especially their integral forms. By making modular reductions including modulo p and modulo p-restrictedness reduction, and base changes, we derive certain modular quantizations of the restricted universal enveloping algebra \mathbf u(K(2n+1;\underline1)) for the restricted simple Lie algebra of Cartan type K in characteristic p. They are new pointed Hopf algebras of noncommutative and noncocommutative and with dimension p^p2n+1+1 (if 2n+4\not≡0 (\mod p)) or p^p2n+1 (if 2n+4≡0 (\mod p)) over a truncated p-polynomials ring, which also contain the well-known Radford algebras as Hopf subalgebras. Some open questions are proposed.