广义latu - igusa - todorov代数与Morita上下文

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-10-14 DOI:10.1007/s10468-024-10289-3

Marcelo Lanzilotta, José Vivero

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引用次数: 0

摘要

本文定义了（特殊）GLIT类和（特殊）GLIT代数。我们证明了推广lati - igusa - todorov代数的GLIT代数满足有限维猜想，并给出了一些性质和例子。此外，我们还证明了特殊的GLIT代数正是具有有限有限维数的代数。最后，我们研究了由Morita上下文产生的Morita代数，并从定义中使用的代数和双模的角度给出了它们是（特殊）GLIT的条件。由此，我们得到了三角矩阵代数为（特殊）GLIT的简单条件，并证明了GLIT \(\mathbb {K}\) -代数与有限无取向环振子的路径代数的张量积是GLIT。

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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Generalised Lat-Igusa-Todorov Algebras and Morita Contexts

In this paper we define (special) GLIT classes and (special) GLIT algebras. We prove that GLIT algebras, which generalise Lat-Igusa-Todorov algebras, satisfy the finitistic dimension conjecture and give several properties and examples. In addition we show that special GLIT algebras are exactly those that have finite finitistic dimension. Lastly we study Morita algebras arising from a Morita context and give conditions for them to be (special) GLIT in terms of the algebras and bimodules used in their definition. As a consequence we obtain simple conditions for a triangular matrix algebra to be (special) GLIT and also prove that the tensor product of a GLIT \(\mathbb {K}\)-algebra with a path algebra of a finite quiver without oriented cycles is GLIT.

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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.