Original title: Gabrielova-Roiterova míra v teorii reprezentací
Translated title: The Gabriel-Roiter measure in representation theory
Authors: Krasula, Dominik ; Šťovíček, Jan (advisor)
Document type: Rigorous theses
Year: 2024
Language: eng
Abstract: [eng] [cze]
The Gabriel-Roiter measure is a module-theoretic invariant, defined in 1972 by P. Gabriel. It is an order-preserving function that refines a composition length of a module by also taking lengths of indecomposable submodules into account. We calculate all Gabriel-Roiter measures for finite-length representa- tions of an orientation of a Dynkin graph D4 and an orientation of a Euclidean graph Ã3. In 2007, H. Krause proposed a combinatorial definition of the Gabriel-Roiter measure based on other length functions instead of composition length. We study these alternative Gabriel-Roiter measures on thin representations of quiv- ers whose underlying graph is a tree. 1 Gabriel-Roiterova míra je invariant na modulech, definovaný v roce 1973 P. Gabrielem. Je to uspořádání-zachovávajicí funkce, která zjemňuje kompoziční délku modulu tím, že bere v potaz též délky nerozložitelných podmodulů. Spočí- táme všechny Gabriel-Roiterovi míry pro reprezentace konečné délky pro konkrét- ní orientaci Dynkinova grafu D4 a Euklidovského grafu Ã3. V roce 2007 H. Krause navrhl kombinatorickou definici Gabriel-Roiterovi míry založenou na jiných funkcích než kompoziční délce. Tyto alternativní Gabriel- Roiterovi míry studujeme na tenkých reprezentacích toulců, které neobsahují neorientované cesty. 1
Keywords: Gabriel-Roiterova míra|reprezentace toulců|tenké reprezentace; Gabriel-Roiter measure|representations of quivers|thin representations

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/190730

Permalink: http://www.nusl.cz/ntk/nusl-622408


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Rigorous theses