莫里塔上下文结构上的 Igusa-Todorov （\phi \）-维度

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-06-13 DOI:10.1007/s10468-023-10218-w

Marcos Barrios, Gustavo Mata

{"title":"莫里塔上下文结构上的 Igusa-Todorov （\\phi \\）-维度","authors":"Marcos Barrios, Gustavo Mata","doi":"10.1007/s10468-023-10218-w","DOIUrl":null,"url":null,"abstract":"<div>In this article we prove that, under certain hypotheses, Morita context algebras with zero bimodule morphisms have finite \\(\\phi \\)-dimension. For these algebras we also study the behaviour of the \\(\\phi \\)-dimension for an algebra and its opposite. In particular we show that the \\(\\phi \\)-dimension of an Artin algebra is not symmetric, i.e. there exists an Artin algebra A such that \\(\\phi \\dim (A) \\not = \\phi \\dim (A^{op})\\).</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"26 6","pages":"3255 - 3269"},"PeriodicalIF":0.5000,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Igusa-Todorov \\\\(\\\\phi \\\\)-Dimension on Morita Context Algebras\",\"authors\":\"Marcos Barrios, Gustavo Mata\",\"doi\":\"10.1007/s10468-023-10218-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>In this article we prove that, under certain hypotheses, Morita context algebras with zero bimodule morphisms have finite \\\\(\\\\phi \\\\)-dimension. For these algebras we also study the behaviour of the \\\\(\\\\phi \\\\)-dimension for an algebra and its opposite. In particular we show that the \\\\(\\\\phi \\\\)-dimension of an Artin algebra is not symmetric, i.e. there exists an Artin algebra A such that \\\\(\\\\phi \\\\dim (A) \\\\not = \\\\phi \\\\dim (A^{op})\\\\).</div>\",\"PeriodicalId\":50825,\"journal\":{\"name\":\"Algebras and Representation Theory\",\"volume\":\"26 6\",\"pages\":\"3255 - 3269\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebras and Representation Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10468-023-10218-w\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebras and Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-023-10218-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在这篇文章中，我们证明了在某些假设条件下，双模态为零的莫里塔上下文代数具有有限的 \(\phi \)-维度。对于这些代数，我们还研究了一个代数及其反面的 \(\phi\)-dimension 的行为。特别是，我们证明了阿尔丁代数的 \(\phi \)-维度不是对称的，也就是说，存在一个阿尔丁代数 A，使得 \(\phi \dim (A) \not = \phi \dim (A^{op})\).

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The Igusa-Todorov \(\phi \)-Dimension on Morita Context Algebras

In this article we prove that, under certain hypotheses, Morita context algebras with zero bimodule morphisms have finite \(\phi \)-dimension. For these algebras we also study the behaviour of the \(\phi \)-dimension for an algebra and its opposite. In particular we show that the \(\phi \)-dimension of an Artin algebra is not symmetric, i.e. there exists an Artin algebra A such that \(\phi \dim (A) \not = \phi \dim (A^{op})\).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.