Twists of quantum Borel algebras

JOURNAL OF ALGEBRA

卷:514

Article

Negron, Cris¹ 

[1] MIT, Dept Math, Cambridge, MA 02139 USA

关键词: Hopf algebras;    Quantum groups;    Drinfeld twists;   

DOI  :  10.1016/j.jalgebra.2018.06.028

来源: Elsevier

【 摘 要 】

We classify Drinfeld twists for the quantum Borel subalgebra u(q)(b) in the Frobenius-Lusztig kernel u(q)(g), where g is a simple Lie algebra over C and q an odd root of unity. More specifically, we show that alternating forms on the character group of the group of grouplikes for u(q)(b) generate all twists for u(q)(b), under a certain algebraic group action. This implies a simple classification of finite-dimensional Hopf algebras whose categories of representations are tensor equivalent to that of u(q)(b). We also show that cocycle twists for the corresponding De Concini-Kac algebra are in bijection with alternating forms on the aforementioned character group. (C) 2018 Published by Elsevier Inc.

【 授权许可】

Free