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

The number of support-tilting modules for a Dynkin algebra

A. A. Obaid M, Khalid Nauman S, M. Fakieh W, Ringel CM. The number of support-tilting modules for a Dynkin algebra. Journal of Integer Sequences. 2015;18(10): 15.10.6