**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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