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arXiv · 2501.05045

Frobenius--Perron dimension via $\tau$-tilting theory

Takahide Adachi·Ryoichi Kase
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Abstract

From the perspective of $\tau$-tilting theory, we study Frobenius--Perron dimensions of finite-dimensional algebras. First, we evaluate the Frobenius--Perron dimensions of $\tau$-tilting finite algebras by a combinatorial method in $\tau$-tilting theory. Secondly, we give the upper bound for the Frobenius--Perron dimension for $\tau$-tilting finite algebras of tame representation type. Thirdly, we determine the Frobenius--Perron dimensions of Nakayama algebras and generalized preprojective algebras of Dynkin type in the sense of Geiss--Leclerc--Schr\"oer.

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BibTeXRIS

Takahide Adachi, Ryoichi Kase. 2025-01-09. Frobenius--Perron dimension via $\tau$-tilting theory. https://arxiv.org/abs/2501.05045

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