The algebraic entropies of the Leavitt path algebra and the graph algebra agree (Q6635280)
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scientific article; zbMATH DE number 7941062
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The algebraic entropies of the Leavitt path algebra and the graph algebra agree |
scientific article; zbMATH DE number 7941062 |
Statements
The algebraic entropies of the Leavitt path algebra and the graph algebra agree (English)
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9 November 2024
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The authors recall the standard filtrations on the path algebra \(KE\) as well as in the Cohn path algebra \(C_K(E)\) and the Leavitt path algebra \(L_K(E)\). They give an expression of entropy in terms of norms of powers of adjacency matrices. Applying the fundamental formula in holomorphic functional calculus to matrices, the authors relate the algebraic entropies of \(C_K(E)\) and \(L_K(E)\) and prove that the algebras \(L_K(E)\) and \(KE\) have the same entropy.
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graph algebra
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path algebra
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Leavitt path algebra
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Gelfand-Kirillov dimension
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algebraic entropy
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