Finite GK-Dimensional Nichols Algebras Over the Infinite Dihedral Group

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-06-29 DOI:10.1007/s10468-023-10213-1

Yongliang Zhang

引用次数: 0

Abstract

We contribute to the classification of Hopf algebras with finite Gelfand-Kirillov dimension, GK-dimension for short, through the study of Nichols algebras over \(\mathbb {D}_{\infty }\), the infinite dihedral group.We find all the irreducible Yetter-Drinfeld modules V over \(\mathbb {D}_{\infty }\), and determine which Nichols algebras \(\mathcal {B}(V)\) of V are finite GK-dimensional.

查看原文本刊更多论文

无限二面体群上的有限GK维Nichols代数

我们通过研究无限二面体群 \(\mathbb {D}_{\infty }\) 上的尼克尔斯代数，为具有有限格尔芬-基里洛夫维度（简称 GK 维度）的霍普夫代数的分类做出了贡献。我们找到了 \(\mathbb {D}_{\infty }\) 上所有不可还原的叶特-德林菲尔德模块 V，并确定了 V 的哪些尼科尔斯代数（\(\mathcal {B}(V)\) 是有限 GK 维的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.