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arXiv · 2006.03634

A note on the regular ideals of Leavitt path algebras

Daniel Gonçalves·Danilo Royer
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Abstract

We show that, for an arbitrary graph, a regular ideal of the associated Leavitt path algebra is also graded. As a consequence, for a row-finite graph, we obtain that the quotient of the associated Leavitt path by a regular ideal is again a Leavitt path algebra and that Condition~(L) is preserved by quotients by regular ideals. Furthermore, we describe the vertex set of a regular ideal and make a comparison between the theory of regular ideals in Leavitt path algebras and in graph C*-algebras.

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Daniel Gonçalves, Danilo Royer. 2020-06-05. A note on the regular ideals of Leavitt path algebras. https://arxiv.org/abs/2006.03634

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