On the Composition of Three Irreducible Morphisms in the Bounded Homotopy Category

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2022-04-26 DOI:10.1007/s10485-022-09682-0

Claudia Chaio, Alfredo González Chaio, Isabel Pratti

引用次数: 1

Abstract

Let \(\Lambda \) be an artin algebra of finite global dimension. We study when the composition of three irreducible morphisms between indecomposable complexes in \({{\mathbf {K}}^{b}(\mathrm {proj}\,\Lambda )}\) is a non-zero morphism in the fourth power of the radical. We apply such results to prove that the composition of three irreducible morphisms between indecomposable complexes in the bounded derived category of a gentle Nakayama algebra, not selfinjective, whose ordinary quiver is an oriented cycle, belongs to the fourth power of the radical if and only if it vanishes.

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关于有界同源范畴中三个不可约态射的合成

设\（\Lambda\）是一个具有有限全局维数的artin代数。我们研究了\（｛｛\mathbf｛K｝｝^｛b｝（\mathrm｛proj｝\，\Lambda）｝\）中不可分解复合物之间的三个不可约态射的组成何时是根的四次方的非零态射。我们应用这些结果证明了一个温和的Nakayama代数的有界导出范畴中的不可分解复形之间的三个不可约态射的组成，而不是自射的，其普通颤动是一个有向循环，属于根的四次方当且仅当它消失。

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.