Uniqueness Theorems and Ideal Structure for Leavitt Path Algebras

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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 $L_\mathbb{C}(E)$ 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).
34 pages, uses XY-pic. New version comments: Some small typos corrected. This is the final version to appear in the Journal of Algebra

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Operator Algebras, Rings and Algebras, 16W50, 46L55

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http://salesiana.dossiersoluciones.com/handle/123456789/124615

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0612628
 http://arxiv.org/abs/math/0612628

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arXiv