# Hopf algebras of discrete representation type

Hopf algebra is an important topic in geometric representation theory. A basic algebra is of finite representation type if there are only finitely many non-isomorphic indecomposable representations. Basic Hopf algebras of finite representation type have been classified by Liu and Li in 2004. As algebras, they are just copies of Nakayama algebras. A pointed coalgebra is of discrete representation type, if there are only finitely many non-isomorphic indecomposable representations for each dimension vector. In this talk, I am going to give a classification of pointed Hopf algebras of discrete representation type. The main tool we are using is called “covering maps” of (finite dimensional) coalgebras which comes from separable extensions of the dual algebras. This is a joint work with Miodrag Iovanov, Emre Sen, and Alexander Sistko.