3-Preprojective Algebras of Type D

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-11-16 DOI:10.1007/s10468-024-10297-3

Jordan Haden

引用次数: 0

Abstract

We present a family of selfinjective algebras of type D, which arise from the 3-preprojective algebras of type A by taking a \(\mathbb {Z}_3\)-quotient. We show that a subset of these are themselves 3-preprojective algebras, and that the associated 2-representation-finite algebras are fractional Calabi-Yau. In addition, we show our work is connected to modular invariants for SU(3).

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D型的3-预投影代数

通过取\(\mathbb {Z}_3\) -商，给出了由a型3预射影代数衍生出的一类D型自射代数。我们证明了这些代数的一个子集本身是3-预投影代数，并且相关的2-表示有限代数是分数阶Calabi-Yau。此外，我们证明了我们的工作与SU(3)的模不变量有关。

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.