A new type restricted quantum group

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI:10.1063/5.0142193

Yongjun Xu, Jialei Chen

引用次数: 1

Abstract

In this paper, we define a new type restricted quantum group Ūq(sl2*) and determine its Hopf Poincaré-Birkhoff-Witt-deformations Ūq(sl2*,κ) in which Ūq(sl2*,0)=Ūq(sl2*) and the classical restricted Drinfeld–Jimbo quantum group Ūq(sl2) is included. We show that Ūq(sl2*) is a basic Hopf algebra, then uniformly realize Ūq(sl2*) and Ūq(sl2) via some quotients of (deformed) preprojective algebras corresponding to the Gabriel quiver of Ūq(sl2*). Moreover, we obtain a uniform tensor-categorical realization of Ūq(sl2*) and Ūq(sl2), which is consistent with the above-mentioned Hopf-algebraic realization.

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一类新型受限量子群

本文定义了一类新的受限量子群Ūq(sl2*)，确定了其Hopf poincar - birkhoff - witt -deformations Ūq(sl2*，κ)，其中Ūq(sl2*，0)=Ūq(sl2*)，并包含经典的受限Drinfeld-Jimbo量子群Ūq(sl2)。首先证明Ūq(sl2*)是一个基本的Hopf代数，然后通过与Ūq(sl2*)的Gabriel颤振相对应的(变形)预投影代数的商统一实现Ūq(sl2*)和Ūq(sl2)。此外，我们得到了Ūq(sl2*)和Ūq(sl2)的一致张量分类实现，这与上述hopf代数实现是一致的。

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 Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.