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arXiv · 2402.18585

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

Wolfgang Bock·Cristóbal Gil Canto·Dolores Martín Barquero·Cándido Martín González·Iván Ruiz Campos·Alfilgen Sebandal
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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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Wolfgang Bock, Cristóbal Gil Canto, Dolores Martín Barquero, Cándido Martín González, Iván Ruiz Campos, Alfilgen Sebandal. 2024-01-15. The algebraic entropies of the Leavitt path algebra and the graph algebras agree. https://arxiv.org/abs/2402.18585

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