RT Journal Article
T1 Algebraic entropy of path algebras and Leavitt path algebras of finite graphs.
A1 Bock, Wolfgang
A1 Gil-Canto, Cristóbal
A1 Martín-Barquero, Dolores
A1 Martín-González, Cándido
A1 Ruiz Campos, Iván
A1 Sebandal, Alfilgen
K1 Anillos (Álgebra)
AB The Gelfand–Kirillov dimension is a well established quantity to classify the growth of infinite dimensional algebras. In this article we introduce the algebraic entropy for path algebras. For the path algebras, Leavitt path algebras and the path algebra of the extended (double) graph, we compare the Gelfand–Kirillov dimension and the entropy. We show that path algebras over finite graphs can be classified to be of finite dimension, finite Gelfand–Kirillov dimension or finite algebraic entropy. We show indeed how these three quantities are dependent on cycles inside the graph. Moreover we show that the algebraic entropy is conserved under Morita equivalence but perhaps for a different filtration. In addition we give several examples of the entropy in path algebras and Leavitt path algebras.
PB Springer Nature
YR 2024
FD 2024
LK https://hdl.handle.net/10630/38169
UL https://hdl.handle.net/10630/38169
LA eng
NO Wolfgang Bock, Cristóbal Gil Canto, Dolores Martín Barquero, Cándido Martín González, Iván Ruiz Campos y Alfilgen Sebandal. Algebraic entropy of path algebras and Leavitt path algebras of finite graphs. Results in Mathematics, 79:180 (2024).
NO PID2019-104236GB-I00/AEI/10.13039/ 501100011033FQM-336UMA18- FEDERJA-119
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026