A survey on representation dimension of artin algebras

This paper deals with representation dimension of artin algebras, a notion defined and studied by M. Auslander. Firstly, we look very briefly at some known results and next present some new results on this issue which aim mainly at obtaining some upper bounds to this number. Our results lie in two different directions: Firstly we focus on algebras which are actually generalized path algebras of cyclic quivers and secondly we consider the general case of Gorenstein artin algebras of finite Cohen-Macaulay type.