© 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).
|Title of host publication||Lecture Notes in Mathematics|
|Number of pages||32|
|Publication status||Published - 1 Jan 2017|
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