矩阵代数嵌入超图莱维特路径代数及其应用

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-07-25 DOI:10.1016/j.laa.2025.07.021

Romar B. Dinoy , Tran Giang Nam , Jocelyn P. Vilela

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引用次数: 0

摘要

本文给出了一个超图G的判据，使得对于任意域K和n≥1，满矩阵代数Mn(K)嵌入到G的相关的Leavitt路径代数中。这一结果在图的Leavitt路径代数中没有出现过，然后应用这一结果表征了Lie可解和Lie幂零超图Leavitt路径代数的性质，并计算了Lie可解超图Leavitt路径代数的可解指标。

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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Embedding matrix algebras into ultragraph Leavitt path algebras and applications

In this article, we provide criteria for an ultragraph

G

so that for any field K and

n \geq 1

, the full matrix algebra

M_{n} (K)

is embedded in the associated Leavitt path algebra of

G

. This result, which has not appeared in the context of Leavitt path algebras of graphs, is then applied to characterize properties of Lie solvable and Lie nilpotent ultragraph Leavitt path algebras, and compute the solvable index of a Lie solvable ultragraph Leavitt path algebra.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.