Worch, Julia
[Author]
;
Farnsteiner, Rolf
[Contributor];
Weidmann, Richard
[Contributor]
Module categories and Auslander-Reiten theory for generalized Beilinson algebras ; Modulkategorien und Auslander-Reiten-Theorie verallgemeinerter Beilinson-Algebren
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Doctoral Thesis;
E-Book;
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Text
Title:
Module categories and Auslander-Reiten theory for generalized Beilinson algebras ; Modulkategorien und Auslander-Reiten-Theorie verallgemeinerter Beilinson-Algebren
Contributor:
Worch, Julia
[Author]
imprint:
MACAU: Open Access Repository of Kiel University, 2013
Footnote:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Description:
Representation theory is concerned with understanding the modules over a given algebra. Two classes of algebras that are frequently studied are group algebras and algebras of finite global dimension, in particular hereditary algebras. In both settings, it is often the case that it is not possible to classify all indecomposable representations, i.e. the algebra is wild. In 2008, Carlson, Friedlander and Pevtsova introduced the class of modules of constant Jordan type as a subclass of the module category over a given group algebra. There is the more restrictive notion of modules with the equal images property. It turns out, however, that these module classes are still very complicated in general. Group algebras of elementary abelian p-groups are of immediate interest in the modular representation theory of finite groups. In a way, they constitute the smallest examples of wild group algebras and by Chouinard's theorem, projectivity of modules over a given group algebra can be tested via restrictions to elementary abelian p-groups. Carlson, Friedlander and Suslin have studied modules with the equal images property and modules of constant Jordan type over k(Z_p \times Z_p). They introduce the so-called W-modules which are prominent examples of modules with the equal images property. The indecomposable k(Z_p \times Z_p)-modules of Loewy length two can be identified with the indecomposables over the hereditary Kronecker algebra, where modules with the equal images property correspond to the preinjective modules. This thesis is inspired by the aim to understand modules with the equal images property over k (Z_p^{\times r}) for arbitrary r. We give a generalization of the W-modules. In order to study k (Z_p^{\times r})-modules with restricted Loewy length, we introduce generalized Beilinson algebras. Making use of a faithful exact functor from the module category of the generalized Beilinson algebra B(n,r) on n vertices into the module category of the group algebra, we define the constant Jordan type property and the ...