On τ\tau-tilting finite simply connected algebras

We show that $\tau$-tilting finite simply connected algebras are representation-finite. Then, some related algebras are considered, including iterated tilted algebras, tubular algebras and so on. We also prove that the $\tau$-tilting finiteness of non-sincere algebras can be reduced to that of sincere algebras. This motivates us to give a complete list of $\tau$-tilting finite sincere simply connected algebras.Comment: 31 page

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τ\tau-tilting finiteness of two-point algebras I

In this paper, we give criteria on $\tau$-tilting finiteness for two kinds of two-point algebras. Moreover, we show the $\tau$-tilting finiteness of some algebras, such as the (infinite-)tame block algebras of Hecke algebras of classical type over an algebraically closed field of characteristic not equal to 2, and the algebras from Table T and Table W introduced by Han [19].Comment: 25 page