The algebraic entropies of the Leavitt path algebra and the graph algebras agree

2024/01/15 by Wolfgang Böck, Cristóbal Gil Canto, Bock, Wolfgang +9
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Mechanics and Applications #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2402.18585

openalex publication_date 2024/01/15 · openalex created_date 2024/03/08 · openalex updated_date 2026/07/28

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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