| dc.description.abstract | In the representation theory of finite dimensional algebras, the fundamental goal is to understand the structure of the category mod⇤ of finite dimensional modules over an algebra ⇤. While solving this problem is difficult in general, there are classes of algebras for which the module category is very well understood. Among these is the class of Nakayama algebras.
A related question, which is also of interest, is to understand the structure of D(⇤), the derived category of mod⇤. This problem is still largely unsolved for Nakayama algebras, and providing some contributions towards that goal is the main aim of this thesis.
The work in this thesis was completed using a combination of di↵erent techniques. We began by developing a form of quiver mutation, which allows us to perform tilting mutation of algebras purely combinatorially, only working with their quivers with relations.
This mutation enabled us to generate chains of derived equivalent algebras, and we used computer assisted search to find such chains going between di↵erent Nakayama algebras. The patterns we observed in the findings from these searches, laid the foundations for many of the results in the second and third papers. | en_US |
