Some remarks on tilting theory

Seminar
Speaker
Prof. Gabriella D'Este (University of Milan)
Date
25/03/2015 - 11:15 - 10:15Add to Calendar 2015-03-25 10:15:00 2015-03-25 11:15:00 Some remarks on tilting theory In the first part of my talk I will describe with few words and many pictures some more or less ‘combinatorial’ results on tilting modules, bimodules and complexes, almost always obtained by means of elementary tools of two types:   - Linear Algebra arguments (that is, comparison of the dimensions of the underlying vector spaces of certain  Hom  and  Ext  groups);   - Representation Theory arguments (that is, analysis of the Auslander - Reiten quivers of suitable finite dimensional algebras, almost always admitting only finitely many indecomposable modules up to isomorphism).    In the second part of my talk I will describe other results (suggested by quivers) concerning ‘reflexive’ modules (not necessarity belonging to the tilting and cotilting worlds) and multiplicities of simple modules in the socle of certain injective cogenerators.  Almost all the results and examples are illustrated in two preprints available at   http://arxiv.org/abs/1401.2085  and   http://arxiv.org/abs/1411.4418 .  Third floor seminar room אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room
Abstract

In the first part of my talk I will describe with few words and many pictures some more or less ‘combinatorial’ results on tilting modules, bimodules and complexes, almost always obtained by means of elementary tools of two types:

 

- Linear Algebra arguments (that is, comparison of the dimensions of the underlying vector spaces of certain 

Hom  and  Ext  groups);

 

- Representation Theory arguments (that is, analysis of the Auslander - Reiten quivers of suitable finite dimensional algebras, almost always admitting only finitely many indecomposable modules up to isomorphism). 

 

In the second part of my talk I will describe other results (suggested by quivers) concerning ‘reflexive’ modules (not necessarity belonging to the tilting and cotilting worlds) and multiplicities of simple modules in the socle of certain injective cogenerators.  Almost all the results and examples are illustrated in two preprints available at  

http://arxiv.org/abs/1401.2085  and  

http://arxiv.org/abs/1411.4418

תאריך עדכון אחרון : 16/03/2015