CRM: Centro De Giorgi
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A cluster algebras day

“Approaches to τ -tilting theory for infinite dimensional algebras”

speaker: Charlotte Ricke (University of Bonn )

abstract: The notion of τ -tilting theory for finite-dimensional algebras was introduced by Adachi, Iyama and Reiten in 2012. The ’slogan’ to keep in mind on τ -tilting theory is that it completes classical tilting theory from the viewpoint of ’mutation’. That is, it yields an appropriate model of the combinatorics of cluster algebras in a module category. In this work we present possible approaches on how to generalise their results to infinite dimensional algebras. We particularly concentrate on a special class of algebras, the (completed) string algebras. Butler and Ringel gave a purely combinatorial description of the finitely generated modules and their Auslander-Reiten sequences for finite-dimensional string algebras. The classification of finitely generated modules was recently generalised by Crawley-Boevey for infinite dimensional string algebras. We now alter his methods to obtain the classification for completed string algebras.

Mon 2 Feb, 16:00 - 16:40, Aula Dini
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