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arXiv · 1907.05969

Skew products of finitely aligned left cancellative small categories and Cuntz-Krieger algebras

Erik Bédos·S. Kaliszewski·John Quigg
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Abstract

Given a group cocycle on a finitely aligned left cancellative small category (LCSC) we investigate the associated skew product category and its Cuntz-Krieger algebra, which we describe as the crossed product of the Cuntz-Krieger algebra of the original category by an induced coaction of the group. We use our results to study Cuntz-Krieger algebras arising from free actions of groups on finitely aligned LCSC's, and to construct coactions of groups on Exel-Pardo algebras. Finally we discuss the universal group of a small category and connectedness of skew product categories.

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Erik Bédos, S. Kaliszewski, John Quigg. 2021-05-21. Skew products of finitely aligned left cancellative small categories and Cuntz-Krieger algebras. https://doi.org/10.17879/59019527597

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