The basics of Leavitt path algebras: Motivations, definitions and examples

Gene Abrams, Pere Ara, Mercedes Siles Molina

Research output: Chapter in BookChapterResearchpeer-review

1 Citation (Scopus)

Abstract

© Springer-Verlag London Ltd. 2017. We introduce the central idea, that of a Leavitt path algebra. We start by describing the classical Leavitt algebras. We then proceed to give the definition of the Leavitt path algebra LK(E) for an arbitrary directed graph E and field K. After providing some basic examples, we show how Leavitt path algebras are related to the monoid realization algebras of Bergman, as well as to graph C∗-algebras. We then introduce the more general construction of relative Cohn path algebras CKX(E), and show how these are related to Leavitt path algebras. We finish by describing how any Cohn (specifically, Leavitt) path algebra may be constructed as a direct limit of Cohn (specifically, Leavitt) path algebras corresponding to finite graphs. We conclude the chapter with an historical overview of the subject.
Original languageEnglish
Title of host publicationLecture Notes in Mathematics
Pages1-31
Number of pages30
Volume2191
DOIs
Publication statusPublished - 1 Jan 2017

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