Leavitt path algebras for power graphs of finite groups
| Autor: | S. K. Maity, Sumanta Das, M. K. Sen |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Algebraic properties
Discrete mathematics Finite group Algebra and Number Theory Computer Science::Information Retrieval Applied Mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Characterization (mathematics) Graph Path algebra Power (physics) TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Path (graph theory) ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Computer Science::General Literature ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Journal of Algebra and Its Applications. 21 |
| ISSN: | 1793-6829 0219-4988 |
| DOI: | 10.1142/s0219498822502097 |
| Popis: | The aim of this paper is the characterization of algebraic properties of Leavitt path algebra of the directed power graph [Formula: see text] and also of the directed punctured power graph [Formula: see text] of a finite group [Formula: see text]. We show that Leavitt path algebra of the power graph [Formula: see text] of finite group [Formula: see text] over a field [Formula: see text] is simple if and only if [Formula: see text] is a direct sum of finitely many cyclic groups of order 2. Finally, we prove that the Leavitt path algebra [Formula: see text] is a prime ring if and only if [Formula: see text] is either cyclic [Formula: see text]-group or generalized quaternion [Formula: see text]-group. |
| Databáze: | OpenAIRE |
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