Delooping Levels

IF 0.6 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2026-02-13 DOI:10.1007/s10468-026-10380-x

Marcos Barrios, Marcelo Lanzilotta, Gustavo Mata

引用次数: 0

Abstract

In (Adv. Math. 394, 108052, 2022) V. Gélinas introduced a homological invariant, called delooping level (dell), that bounds the finitistic dimension. In this article, we introduce another homological invariant (Dell) related to the delooping level for an Artin algebra. We compare this new tool with other dimensions as the finitistic dimension or the \(\varvec{\phi }\)-dimension (where \(\varvec{\phi }\) is the first Igusa-Todorov function), and we also generalize Theorem 4.3. from Gélinas (Proc. Amer. Math. Soc. 149(12), 5001–5012, 2021) to truncated path algebras (Theorem 4.18). Finally, we show that for a monomial algebra \(\varvec{A}\) the difference \(\text{ dell }\varvec{(A)} \varvec{-} \text{ Findim }\varvec{(A)}\) can be arbitrarily large (Example 4.22).

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Delooping关卡

在（Adv. Math. 394, 108052,2022）中，V. g linas引入了一个称为发展水平（dell）的同调不变量，它限制了有限维。在本文中，我们引入了另一个与Artin代数的展开水平相关的同调不变量（Dell）。我们将这个新工具与其他维度进行比较，如有限维度或\(\varvec{\phi }\) -维度（其中\(\varvec{\phi }\)是第一个Igusa-Todorov函数），并且我们也推广了定理4.3。源自gsamina（美国程序）数学。物理学报，149(12),5001-5012,2021)到截断路径代数（定理4.18）。最后，我们展示了对于单项式代数\(\varvec{A}\)，差异\(\text{ dell }\varvec{(A)} \varvec{-} \text{ Findim }\varvec{(A)}\)可以任意大（例4.22）。

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.