On the General Ranks of QP Representations

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-01-04 DOI:10.1007/s10468-024-10306-5

JiaRui Fei

引用次数: 0

Abstract

We propose a mutation formula for the general rank from a principal component \({{\,\textrm{PC}\,}}(\delta )\) of representations to another one \({{\,\textrm{PC}\,}}({\epsilon })\) for a quiver with potential. We give sufficient conditions for the formula to hold. In particular, the formula holds when any of \(\delta \) and \({\epsilon }\) is reachable. We discover several related mutation invariants.

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我们提出了一个突变公式，用于从一个主成分（{{\textrm{PC}\,}}(\delta )）表示到另一个主成分（{{\textrm{PC}\,}}({\epsilon })）表示的一般秩，用于一个有势能的奎伍。我们给出了公式成立的充分条件。特别是，当 \(\delta \) 和 \({\epsilon }\) 中的任何一个是可达到的时候，公式成立。我们发现了几个相关的突变不变式。

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.