Leavitt path algebras with bounded index of nilpotence and simple modules over them

2016/11/23 by Kulumani M. Rangaswamy, Rangaswamy, Kulumani M., Ashish K. Srivastava +1 · 1 citation
Mathematics · #16D50 #16D60 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16D50 #msc:16D60

paper · pdf · doi:10.48550/arxiv.1611.07858

arxiv created 2016/11/23 · arxiv updated 2016/11/24

Abstract

In this paper we completely describe graphically Leavitt path algebras with bounded index of nilpotence and show that each graded simple module S over a Leavitt path algebra with bounded index of nilpotence is graded Σ-injective, that is, S^(α) is graded injective for any cardinal α. Furthermore, we characterize Leavitt path algebras over which each simple module is Σ-injective. We have shown that each simple module over a Leavitt path algebra L_K(E) is Σ-injective if and only if the graph E contains no cycles, and there is a positive integer d such that the length of any path in E is less than or equal to d and the number of distinct paths ending at any vertex v (including v) is less than or equal to d.

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• Leavitt path algebras with bounded index of nilpotence

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