PUB - Publikationen an der Universität Bielefeld

In this thesis we study representation theoretic aspects of persistence modules. The first subject is an investigation of the spectrum of the category of vector space representations of a totally ordered set $T$: We show the existence of and determine the spectrum of this category in the sense of Krause and Herzog, and then show that it is homeomorphic to the space of ideals of $T$ equipped with the order topology. Using this homeomorphism we then study its further properties. The second subject concerns the theory of middle exact representations: We generalise and discuss the notions of middle exactness and block representations from two- to three-parameter persistence modules and generalise the decomposition theorem of Botnan and Crawley-Boevey to this case. Both of this is complemented by a discussion of the representation theoretic foundations of persistence modules in terms of functor categories, reviewing their calculus, decomposition theory and homological properties.