| In this thesis we study two types of complexity of modules over finite-dimensional algebras.;In the first part, we examine the O-complexity of a family of self-injective k-algebras where k is an algebraically closed field and O is the syzygy operator. More precisely, let T be the trivial extension of an iterated tilted algebra of type H. We prove that modules over the trivial extension T all have complexities either 0, 1, 2 or infinity, depending on the representation type of the hereditary algebra H. As part of the proof, we show that a stable equivalence between self-injective algebras preserves the complexity of modules.;In the second part, we study the tau-complexity of modules over cluster tilted algebras where tau is the Auslander-Reiten translate. We prove that modules over the cluster tilted algebra of type H all have complexities either 0, 1, 2 or infinity, depending on the representation type of the hereditary algebra H. |
