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SUMMARY:Teresa Conde (University of Stuttgart)
DTSTART:20200821T170000Z
DTEND:20200821T174000Z
DTSTAMP:20260415T214236Z
UID:EVAH2020/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EVAH2020/6/"
 >The Gabriel-Roiter measure and the finiteness of the representation dimen
 sion</a>\nby Teresa Conde (University of Stuttgart) as part of Encuentro V
 irtual de Álgebra Homológica\n\n\nAbstract\nThe induction scheme used in
  Roiter's proof of the first Brauer-Thrall conjecture prompted Gabriel to 
 introduce an invariant\, known as the Gabriel-Roiter measure. The usefulne
 ss of the Gabriel-Roiter measure is not limited to the first Brauer-Thrall
  conjecture: Ringel has used it to give new proofs of results established 
 by himself\, Auslander and Tachikawa in the 70's. It turns out that the Ga
 briel-Roiter measure can also be used to provide an alternative proof of t
 he finiteness of the representation dimension for Artin algebras\, a resul
 t originally shown by Iyama in 2002. The concept of Gabriel-Roiter measure
  can be extended to abelian length categories and every such category has 
 multiple Gabriel-Roiter measures. The aim of this talk is to clarify the f
 ollowing refined version of Iyama's theorem: given any object X and any Ga
 briel-Roiter measure m in an abelian length category\, there exists an obj
 ect X' which depends on X and m\, such that the endomorphism ring of the d
 irect sum of X with X' is quasihereditary\, and hence has finite global di
 mension.\n
LOCATION:https://researchseminars.org/talk/EVAH2020/6/
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