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Graph C ∗-Algebras, and Their Relationship to Leavitt Path Algebras

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Book cover Leavitt Path Algebras

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2191))

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Abstract

In this chapter we investigate the connections between Leavitt path algebras (with coefficients in \(\mathbb{C}\)), and their analytic counterparts, the graph C ∗-algebras. We start by giving a brief overview of graph C ∗-algebras, and then show how the Leavitt path algebra \(L_{\mathbb{C}}(E)\) naturally embeds as a dense ∗-subalgebra of the graph C ∗-algebra C ∗(E). We analyze the structure of the closed ideals in C ∗(E) for row-finite graphs, and compare this structure to the ideal structure of the corresponding Leavitt path algebra L K (E). We finish the chapter by considering numerous properties which are simultaneously shared by C ∗(E) and \(L_{\mathbb{C}}(E)\).

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Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Colorado Springs, USA

    Gene Abrams

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

    Pere Ara

  3. Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Málaga, Spain

    Mercedes Siles Molina

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  1. Gene Abrams
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  2. Pere Ara
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  3. Mercedes Siles Molina
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Abrams, G., Ara, P., Siles Molina, M. (2017). Graph C ∗-Algebras, and Their Relationship to Leavitt Path Algebras. In: Leavitt Path Algebras. Lecture Notes in Mathematics, vol 2191. Springer, London. https://doi.org/10.1007/978-1-4471-7344-1_5

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