Abstract
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 algebra 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 ) .
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