Uniqueness theorems and ideal structure for Leavitt path algebras

[摘要] We prove Leavitt path algebra versions of the two uniqueness theorems of graph C*-algebras. We use these uniqueness theorems to analyze the ideal structure of Leavitt path algebras and give necessary and sufficient conditions for their simplicity. We also use these results to give a proof of the fact that for any graph E the Leavitt path aluebra L-C(E) embeds as a dense *-subalgebra of the graph C*-algebra C*(E). This embedding has consequences for graph C*-algebras, and we discuss how we obtain new information concerning the construction of C*(E). (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-01

[关键词] C*-algebra;Z-graded ring;Z-graded algebra;Leavitt path algebra;graph algebra;ideal structure;uniqueness theorems