On String Algebras and the Cohen–Macaulay Auslander Algebras

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-07-09 DOI:10.1007/s10485-024-09779-8

Yu-Zhe Liu, Chao Zhang

引用次数: 0

Abstract

The Cohen–Macaulay Auslander algebra of an algebra A is defined as the endomorphism algebra of the direct sum of all indecomposable Gorenstein projective A-modules. The Cohen–Macaulay Auslander algebra of any string algebra is explicitly constructed in this paper. Moreover, it is shown that a class of special string algebras, which are called to be string algebras satisfying the G-condition, are representation-finite if and only if their Cohen–Macaulay Auslander algebras are representation-finite. As applications, it is proved that the derived representation type of gentle algebras coincide with their Cohen–Macaulay Auslander algebras.

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论弦代数与科恩-麦考莱奥斯兰德代数

代数 A 的 Cohen-Macaulay Auslander 代数被定义为所有不可分解的 Gorenstein 投影 A 模块的直和的内构代数。本文明确地构造了任何弦代数的 Cohen-Macaulay Auslander 代数。此外，本文还证明，当且仅当它们的 Cohen-Macaulay Auslander 代数是表征无限的时候，一类特殊的弦代数，即满足 G 条件的弦代数，才是表征无限的。作为应用，证明了温柔代数的派生表示类型与它们的科恩-麦考莱-奥斯兰德代数重合。

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

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.