In a recent paper, Pardo and the first named author introduced a class of C*-algebras which are constructed from an action of a group on a graph. This class was shown to include many C*-algebras of interest, including all Kirchberg algebras in the UCT class. In this paper, we study the conditions under which these algebras can be realized as partial crossed products of commutative C*-algebras by groups. In addition, for any n ≥ 2 we present a large class of groups such that for any group H in this class, the Cuntz algebra On is isomorphic to a partial crossed product of a commutative C*-algebra by H.

C*-algebra, Inverse semigroup, Partial crossed product, Self-similar group
dx.doi.org/10.7900/jot.2015mar04.2072
Journal of Operator Theory

Exel, R. (Ruy), & Starling, C. (2016). Self-similar graph C*-algebras and partial crossed products. Journal of Operator Theory, 75(2), 299–317. doi:10.7900/jot.2015mar04.2072