@inbook{10498/37531,
year = {2025},
url = {http://hdl.handle.net/10498/37531},
abstract = {In these notes, we introduce the concept of self-similar graph, associated with groups acting on graphs. We define the corresponding C*-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.},
organization = {The author was partially supported by PAIDI grant FQM-298 of the Junta de Andalucía, by the Spanish State Research Agency (through grant number PID2023-147110NB-I00), and by the grant ``Operator Theory: an interdisciplinary approach'', reference ProyExcel 00780 of the Plan Andaluz de Investigación, Desarrollo e Innovación (PAIDI 2020), Consejería de Universidad, Investigación e Innovación of the Junta de Andalucía.},
publisher = {Repositorio Científico arXiv},
keywords = {Self-similar group},
keywords = {Nekrashevych algebras},
keywords = {Katsura algebras},
keywords = {Self-similar graph},
keywords = {Inverse semigroup},
keywords = {Tight groupoid},
keywords = {groupoid C*-algebra},
keywords = {Steinberg algebra},
keywords = {k-graph},
keywords = {Twisted groupoid},
keywords = {Left cancellative small category},
keywords = {Zappa-Szép product},
keywords = {Groupoid homology},
keywords = {K-theory},
title = {An overview on self-similar graphs, their generalizations, and their associated algebras.},
doi = {10.48550/arXiv.2509.18702},
author = {Pardo Espino, Enrique},
}