2026-05-29T23:30:57Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/381692026-02-03T10:51:39Zcom_10630_2254col_10630_37953

Algebraic entropy of path algebras and Leavitt path algebras of finite graphs. Bock, Wolfgang Gil-Canto, Cristóbal Martín-Barquero, Dolores Martín-González, Cándido Ruiz Campos, Iván Sebandal, Alfilgen Anillos (Álgebra) 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. 2025-03-19T12:24:29Z 2025-03-19T12:24:29Z 2024 journal article 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). https://hdl.handle.net/10630/38169 10.1007/s00025-024-02198-0 eng http://creativecommons.org/licenses/by/4.0/ open access Attribution 4.0 Internacional Springer Nature