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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.18585 |
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| _version_ | 1866914704536895488 |
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| author | Bock, Wolfgang Canto, Cristóbal Gil Barquero, Dolores Martín González, Cándido Martín Campos, Iván Ruiz Sebandal, Alfilgen |
| author_facet | Bock, Wolfgang Canto, Cristóbal Gil Barquero, Dolores Martín González, Cándido Martín Campos, Iván Ruiz Sebandal, Alfilgen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The algebraic entropies of the Leavitt path algebra and the graph algebras agree Bock, Wolfgang Canto, Cristóbal Gil Barquero, Dolores Martín González, Cándido Martín Campos, Iván Ruiz Sebandal, Alfilgen Rings and Algebras 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. |
| title | The algebraic entropies of the Leavitt path algebra and the graph algebras agree |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2402.18585 |