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2017 | OriginalPaper | Chapter

1. The Basics of Leavitt Path Algebras: Motivations, Definitions and Examples

Authors : Gene Abrams, Pere Ara, Mercedes Siles Molina

Published in: Leavitt Path Algebras

Publisher: Springer London

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Abstract

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 L K (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 C K X (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.

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Metadata
Title
The Basics of Leavitt Path Algebras: Motivations, Definitions and Examples
Authors
Gene Abrams
Pere Ara
Mercedes Siles Molina
Copyright Year
2017
Publisher
Springer London
Book
Leavitt Path Algebras

Print ISBN: 978-1-4471-7343-4

Electronic ISBN: 978-1-4471-7344-1

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-1-4471-7344-1_1

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