The Arens-Michael envelopes of the Jordan plane and U q ( s l ( 2 ) ) U_q(\mathfrak{sl}(2)) U q ​ ( sl ( 2 ))

Journal of noncommutative geometry

article

Dmitrii Pedchenko¹ 

[1] The Pennsylvania State University, University Park

关键词: Arens-Michael functor;    Arens-Michael envelope;    Ore extension;    noncommutative geometry;   

DOI  :  10.4171/jncg/461

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

The Arens-Michael functor in noncommutative geometry is an analogue of the analytification functor in algebraic geometry: out of the ring of “algebraic functions” on a noncommutative affine scheme, it constructs the ring of “holomorphic functions” on it when viewed as a noncommutative complex analytic space. In this paper, we explicitly compute the Arens-Michael envelopes of the Jordan plane and the quantum enveloping algebra Uq(sl(2))U_q(\mathfrak{sl}(2))Uq​(sl(2)) of sl(2)\mathfrak{sl}(2)sl(2) for ∣q∣=1|q|=1∣q∣=1.

【 授权许可】

CC BY