Frobenius--Perron dimension via $\ddot{I}„$-tilting theory

Abstract

From the perspective of $\ddot{I}„$-tilting theory, we study Frobenius--Perron dimensions of finite-dimensional algebras. First, we evaluate the Frobenius--Perron dimensions of $\ddot{I}„$-tilting finite algebras by a combinatorial method in $\ddot{I}„$-tilting theory. Secondly, we give the upper bound for the Frobenius--Perron dimension for $\ddot{I}„$-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--Schröer.