The Algebraic Entropies of the Leavitt Path Algebra and the Graph Algebra Agree
Dolores Martín Barquero, Wolfgang Bock, Iván Ruiz Campos, Cristóbal Gil Canto, Cándido Martín González, Alfilgen Sebandal
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Source: Crossref
Published: Oct 24, 2024
DOI: 10.1007/s00025-024-02289-y
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Abstract In this note we prove that the algebras L K ( E ) and KE have the same entropy. Entropy is always referred to the standard filtrations in the corresponding kind of algebra. The main argument leans on (1) the holomorphic functional calculus; (2) the relation of entropy with suitable norm of the adjacency matrix; and (3) the Cohn path algebras which yield suitable bounds for the algebraic entropies.
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