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On finitely aligned left cancellative small categories, Zappa-Sz\'ep products and Exel-Pardo algebras

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arxiv 1712.09432 v2 pith:YVGGJOSL submitted 2017-12-26 math.OA

Erik Bédos , S. Kaliszewski , John Quigg , Jack Spielberg This is my paper · ORCID
classification math.OA
keywords algebrascancellativecategoriesleftsmallalignedcasecategory
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abstract

We consider Toeplitz and Cuntz-Krieger $C^*$-algebras associated with finitely aligned left cancellative small categories. We pay special attention to the case where such a category arises as the Zappa-Sz\'ep product of a category and a group linked by a one-cocycle. As our main application, we obtain a new approach to Exel-Pardo algebras in the case of row-finite graphs. We also present some other ways of constructing $C^*$-algebras from left cancellative small categories and discuss their relationship.

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  1. Subshift semigroups

    math.OA 2019-08 accept novelty 7.0 of 10

    For every subshift, the Matsumoto and Carlsen-Matsumoto C*-algebras are realized as groupoid C*-algebras from the inverse hull of the language semigroup, and this universal groupoid is amenable.

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