A talented monoid view on Lie bracket algebras over Leavitt path algebras

被引：3

作者：

Bock, Wolfgang ^{[1
]}

Sebandal, Alfilgen ^{[2
]}

Vilela, Jocelyn ^{[2
]}

机构：

[1] Tech Univ Kaiserslautern, Dept Math, Gottlieb Daimler Str 48, D-67663 Kaiserslautern, Germany

[2] MSU Iligan Inst Technol, Ctr Graph Theory Algebra & Anal, Premier Res Inst Sci & Math, Dept Math & Stat,Coll Sci & Math, Iligan 9200, Philippines

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2023年 / 22卷 / 08期

关键词：

Leavitt path algebra; Lie algebra; talented monoid; CLASSIFICATION;

D O I：

10.1142/S0219498823501700

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study properties such as simplicity, solvability and nilpotency for Lie bracket algebras arising from Leavitt path algebras, based on the talented monoid of the underlying graph. We show that graded simplicity and simplicity of the Leavitt path algebra can be connected via the Lie bracket algebra. Moreover, we use the Gelfand-Kirillov dimension for the Leavitt path algebra for a classification of nilpotency and solvability.

引用

页数：21

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