A survey of some of the recent developments in Leavitt path algebras

2018/08/13 by Kulumani M. Rangaswamy, Rangaswamy, Kulumani M.
Mathematics · #16G20 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1808.04466

openalex publication_date 2018/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This survey of the recent developments in the investigations of a Leavitt path algebra L of an arbitrary graph E over a field K consists of two parts. In the first part describes how very often a single graph property of E implies multiple ring properties of L, thus making Leavitt path algebras effective tools in constructing rings of various desirable properties. The second part describes methods of constructing simple modules over L and characterizes Leavitt path algebras all of whose simple modules possess some specific properties such as being flat, finitely presented,being graded, injective etc.

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