Complexity over Finite-Dimensional Algebras

<p>In this thesis we study two types of complexity of modules over finite-dimensional algebras.</p> <p>In the first part, we examine the Ω-complexity of a family of self-injective k-algebras where k is an algebraically closed field and Ω 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.</p> <p>In the second part, we study the τ-complexity of modules over cluster tilted algebras where τ 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.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2011

Author dc:creator

• Purin, Marju

Contributors dc:contributor

• Dan Zacharia

• cluster tilted algebra
• complexity
• finite-dimensional algebra
• tilting theory
• trivial extension
• Mathematics

Repository record dc:identifier

https://surface.syr.edu/mat_etd/62

OAI identifier oai:identifier

oai:surface.syr.edu:mat_etd-1062