RT book part
T1 An overview on self-similar graphs, their generalizations, and their associated algebras.
A1 Pardo Espino, Enrique
A2 Matemáticas
K1 Self-similar group
K1 Nekrashevych algebras
K1 Katsura algebras
K1 Self-similar graph
K1 Inverse semigroup
K1 Tight groupoid
K1 groupoid C*-algebra
K1 Steinberg algebra
K1 k-graph
K1 Twisted groupoid
K1 Left cancellative small category
K1 Zappa-Szép product
K1 Groupoid homology
K1 K-theory
AB 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.
PB Repositorio Científico arXiv
YR 2025
FD 2025
LK http://hdl.handle.net/10498/37531
UL http://hdl.handle.net/10498/37531
LA eng
NO 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.
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026