Structural properties of C*-Algebras such as Stable Rank One, Real Rank Zero, and radius of comparison have played an important role in classification.  Crossed product C*-Algebras are useful examples to study because knowledge of the base Algebra can be leveraged to determine properties of the crossed product.  In this talk we will discuss the permanence of various structural properties when taking crossed products of several types.  Crossed products considered will include the usual C* crossed product by a group action along with generalizations such as crossed products by a partial automorphism.  

This talk is based on joint work with Julian Buck and N. Christopher Phillips and on joint work with Maria Stella Adamo, Marzieh Forough, Magdalena Georgescu, Ja A Jeong, Karen Strung, and Maria Grazia Viola.

The Zappa–Szép (ZS) product of two groupoids is a generalization of the semi-direct product: instead of encoding one groupoid action by homomorphisms, the ZS product groupoid encodes two (non-homomorphic, but “compatible”) actions of the groupoids on each other. I will show how to construct the ZS product of two twists over such groupoids and give an example using Weyl twists from Cartan pairs arising from Kumjian--Renault theory.

 Based on joint work with Boyu Li, New Mexico State University

A self-similar k-graph is a pair consisting of a (discrete countable) group and a k-graph, such that the group acts on the k-graph self-similarly. For such a pair, one can associate it with a universal C*-algebra, called the self-similar k-graph C*-algebra. This class of C*-algebras embraces many important and interesting C*-algebras,  such as the higher rank graph C*-algebras of Kumjian-Pask, the Katsura algebras,  the Nekrashevych algebras constructed from self-similar groups, and the Exel-Pardo algebra. 

In this talk, we will survey some results on self-similar k-graph C*-algebras.