Graph C -algebras, and their relationship to Leavitt path algebras

Gene Abrams, Pere Ara, Mercedes Siles Molina

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2 Citations (Scopus)

Abstract

© Springer-Verlag London Ltd. 2017. In this chapter we investigate the connections between Leavitt path algebras (with coefficients in 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 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 ℂ (E).
Original languageEnglish
Title of host publicationLecture Notes in Mathematics
Pages185-217
Number of pages32
Volume2191
DOIs
Publication statusPublished - 1 Jan 2017

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    Abrams, G., Ara, P., & Siles Molina, M. (2017). Graph C -algebras, and their relationship to Leavitt path algebras. In Lecture Notes in Mathematics (Vol. 2191, pp. 185-217) https://doi.org/10.1007/978-1-4471-7344-1_5