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

共 50 条

[41] Injectives over Leavitt path algebras of graphs with disjoint cycles
Abrams, Gene
Mantese, Francesca
Tonolo, Alberto
JOURNAL OF PURE AND APPLIED ALGEBRA, 2024, 228 (07)
[42] The talented monoid of a directed graph with applications to graph algebras
Cordeiro, Luiz Gustavo
Goncalves, Daniel
Hazrat, Roozbeh
REVISTA MATEMATICA IBEROAMERICANA, 2022, 38 (01) : 223 - 256
[43] The graded structure of Leavitt path algebras
R. Hazrat
Israel Journal of Mathematics, 2013, 195 : 833 - 895
[44] Leavitt path algebras of quantum quivers
Graham, Joshua
Goswami, Rishabh
Palin, Jason
ARCHIV DER MATHEMATIK, 2025, 124 (01) : 29 - 48
[45] Distinguishing Leavitt algebras among Leavitt path algebras of finite graphs by the Serre property
Hazrat, Roozbeh
Rangaswamy, Kulumani M.
ARCHIV DER MATHEMATIK, 2023, 121 (2) : 133 - 143
[46] Distinguishing Leavitt algebras among Leavitt path algebras of finite graphs by the Serre property
Roozbeh Hazrat
Kulumani M. Rangaswamy
Archiv der Mathematik, 2023, 121 : 133 - 143
[47] Using Steinberg algebras to study decomposability of Leavitt path algebras
Clark, Lisa Orloff
Barquero, Dolores Martin
Gonzalez, Cÿndido Martin
Molina, Mercedes Siles
FORUM MATHEMATICUM, 2017, 29 (06) : 1311 - 1324
[48] Crossed product Leavitt path algebras
Hazrat, Roozbeh
Vas, Lia
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2021, 31 (08) : 1753 - 1773
[49] Strongly graded Leavitt path algebras
Lundstrom, Patrik
Oinert, Johan
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022, 21 (07)
[50] Classification conjectures for Leavitt path algebras
Cortinas, Guillermo
Hazrat, Roozbeh
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2024,

← 1 2 3 4 5 →