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arXiv · 1902.02583

The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations

Mark V Lawson·Alina Vdovina
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Abstract

This paper is a contribution to the theory of what might be termed $0$-dimensional non-commutative spaces. We prove that associated with each inverse semigroup $S$ is a Boolean inverse semigroup presented by the abstract versions of the Cuntz-Krieger relations. We call this Boolean inverse semigroup the Exel completion of $S$ and show that it arises from Exel's tight groupoid under non-commutative Stone duality.

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Mark V Lawson, Alina Vdovina. 2019-02-07. The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations. https://arxiv.org/abs/1902.02583

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