Global dimension of Nakayama algebras

Uematsu and Yamagata proved that a Nakayama algebra is quasi-hereditary if and only if there is a simple module of projective dimension two. In an earlier paper I proved that a Nakayama algebra is of finite global dimension if and only if there is a simple module of even projective dimension. In this talk I will discuss the above and the following new result. Let A be a Nakayama algebra with n non-isomorphic simple modules, one of the simple modules having even projective dimension 2m. Then the global dimension of A is bounded by n+m–1. This is joint work with Rene Marczinzik.