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arXiv · 2106.06036

Leavitt path algebras of labelled graphs

Giuliano Boava·Gilles G. de Castro·Daniel Gonçalves·Daniel W. van Wyk
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Abstract

A Leavitt labelled path algebra over a commutative unital ring is associated with a labelled space, generalizing Leavitt path algebras associated with graphs and ultragraphs as well as torsion-free commutative algebras generated by idempotents. We show that Leavitt labelled path algebras can be realized as partial skew group rings, Steinberg algebras, and Cuntz-Pimsner algebras. Via these realizations we obtain generalized uniqueness theorems, a description of diagonal preserving isomorphisms and we characterize simplicity of Leavitt labelled path algebras. In addition, we prove that a large class of partial skew group rings can be realized as Leavitt labelled path algebras.

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Giuliano Boava, Gilles G. de Castro, Daniel Gonçalves, Daniel W. van Wyk. 2021-06-10. Leavitt path algebras of labelled graphs. https://arxiv.org/abs/2106.06036

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