### 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 language | English |
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Title of host publication | Lecture Notes in Mathematics |

Pages | 185-217 |

Number of pages | 32 |

Volume | 2191 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

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## Cite this

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