Rigid analytic quantum groups and quantum Arens-Michael envelopes

JOURNAL OF ALGEBRA

卷:537

Article

Dupre, Nicolas¹ 

[1] Ctr Math Sci, Dept Pure Math & Math Stat, Wilberforce Rd, Cambridge CBS 0WB, England

关键词: Quantum groups;    p-adic number theory;    Representation theory;    BGG theory;   

DOI  :  10.1016/j.jalgebra.2019.06.037

来源: Elsevier

【 摘 要 】

We introduce a rigid analytification of the quantized coordinate algebra of a semisimple algebraic group and a quantized Arens-Michael envelope of the enveloping algebra of the corresponding Lie algebra, working over a non-archimedean field and when q is not a root of unity. We show that these analytic quantum groups are topological Hopf algebras and Frechet-Stein algebras. We then introduce an analogue of the BGG category O for the quantum Arens-Michael envelope and show that it is equivalent to the category O for the corresponding quantized enveloping algebra. (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free