An overview on self-similar graphs, their generalizations, and their associated algebras

Abstract

In these notes, we introduce the concept of self-similar graph, associated with groups acting on graphs. We define the corresponding C${}^{\ast }$-algebra using different complementary approaches to understand its basic properties. We also analyze various generalizations that appear in the literature and, in particular, review the relationship of this construction with Zappa–Szép products. Finally, we present very recent results on homology and K-theory for these algebras.