On finitely aligned left cancellative small categories, Zappa-Szép products and Exel-Pardo algebras

Abstract

We consider Toeplitz and Cuntz-Krieger $C^{\ast }$-algebras associated with finitely aligned left cancellative small categories. We pay special attention to the case where such a category arises as the Zappa-Szép 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 $C^{\ast }$-algebras from left cancellative small categories and discuss their relationship.

60 pages. Sections 3 and 4 have been switched, and a remark (Remark 4.2) has been added, as suggested by the referees