Hopf Algebra (Co)actions on Rational Functions

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-11-23 DOI:10.1007/s10468-024-10294-6

Ulrich Krähmer, Blessing Bisola Oni

引用次数: 0

Abstract

In the theory of quantum automorphism groups, one constructs Hopf algebras acting on an algebra K from certain algebra morphisms \( \sigma :K \rightarrow \textrm{M}_n(K)\). This approach is applied to the field \(K=k(t)\) of rational functions, and it is investigated when these actions restrict to actions on the coordinate ring \(B=k[t^2,t^3]\) of the cusp. An explicit example is described in detail and shown to define a new quantum homogeneous space structure on the cusp.

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有理函数上的Hopf代数（Co）作用

在量子自同构群理论中，从若干代数态射\( \sigma :K \rightarrow \textrm{M}_n(K)\)构造作用于代数K的Hopf代数。将此方法应用于有理函数的\(K=k(t)\)域，并研究了这些作用何时限制为顶点坐标环\(B=k[t^2,t^3]\)上的作用。详细描述了一个明确的例子，并展示了在尖端上定义一个新的量子齐次空间结构。

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

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.