2008•Publikationen an der Universität Bielefeld (Universität Bielefeld)Open access

Infinite Gabriel-Roiter measures for the 3-Kronecker quiver

Philipp Fahr

Abstract

In this thesis we will use indecomposable representations of the 3-Kronecker quiver to construct uncountably many infinite Gabriel-Roiter measures. Our aim is to classify all piling submodules of an indecomposable regular module. We will show that they are either unique of a certain length or there is a one-parameter family of such submodules. A possible largest Gabriel-Roiter measure in the central part is discussed.

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Key concepts: Quiver, Indecomposable module, Kronecker delta, Mathematics, Measure (data warehouse), Construct (python library), Pure mathematics, Algebra over a field