Geodesic
On finitely aligned left cancellative small categories, Zappa-Szep products and Exel-Pardo algebras
Theory and applications of categories, Tome 33 (2018), pp. 1346-1406

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We consider Toeplitz and Cuntz-Krieger $C^*$-algebras associated with fin\-itely aligned left cancellative small categories. We pay special attention to the case where such a category arises as the Zappa-Szep 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.

Publié le :
Classification : 46L05, 46L55
Keywords: Groups, graphs, self-similarity, category of paths, left cancellative small categories, Zappa-Szep products, Toeplitz algebras, Cuntz-Krieger algebras 
@article{TAC_2018_33_a41,
     author = {Erik Bedos and S. Kaliszewski and John Quigg and Jack Spielberg},
     title = {On finitely aligned left cancellative small categories, {Zappa-Szep
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     journal = {Theory and applications of categories},
     pages = {1346--1406},
     publisher = {mathdoc},
     volume = {33},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a41/}
}
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Erik Bedos; S. Kaliszewski; John Quigg; Jack Spielberg. On finitely aligned left cancellative small categories, Zappa-Szep
products and Exel-Pardo algebras. Theory and applications of categories, Tome 33 (2018), pp. 1346-1406. http://geodesic.mathdoc.fr/item/TAC_2018_33_a41/