The Arens-Michael envelopes of the Jordan plane and $U_q(\mathfrak{sl}(2))$

IF 0.7 2区数学 Q2 MATHEMATICS Journal of Noncommutative Geometry Pub Date : 2020-09-14 DOI:10.4171/jncg/461

Dmitrii Pedchenko

引用次数: 0

Abstract

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 space it constructs the ring of "holomorphic functions" on it. In this paper, we explicitly compute the Arens-Michael envelopes of the Jordanian plane and the quantum enveloping algebra $U_q(\mathfrak{sl}(2))$ of $\mathfrak{sl}(2)$ for $|q|=1$.

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Jordan平面的Arens-Michael包络和$U_q（\mathfrak｛sl｝（2））$

非交换几何中的Arens-Michael函子是代数几何中的分析函子的类似物:它从非交换空间上的“代数函数”环中构造出该空间上的“全纯函数”环。本文明确地计算了约旦平面的Arens-Michael包络和$\mathfrak{sl}(2)$的$\mathfrak{sl}(2)$的量子包络代数$U_q(\mathfrak{sl}(2))$对于$|q|=1$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.