Résumé: Let A be a finite-dimensional associative algebra over a field. A family of subcategories of A-modules (known as torsion classes) are known to form a lattice under inclusion. In several recent papers, this lattice has been studied using « brick labeling », a method of associating a special type of module (called a brick) to each cover relation in the lattice. A collection of these bricks labels the « downward » (resp. « upward ») cover relations of some element of the lattice if and only if there are no nontrivial morphisms between them. In this talk, we consider the bricks labeling both « downward » and « upward » cover relations at the same time. More precisely, if we are given two sets of bricks D and U, we formulate necessary and sufficient algebraic conditions for there to exist a torsion class T so that the bricks in D label cover relations of the form T’ < T and the bricks in U label cover relations of the form T < T ». This is based on joint works with Emily Barnard and Kiyoshi Igusa.
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23 octobre Vendredi
Eric Hanson (Brandeis): Canonical join and meet representations in lattices of torsion classes
23 octobre 2020, 11:00 - 23 octobre 2020, 12:00
En ligne/online, Canada
Date : octobre 23, 2020
Heure : 11:00 am - 12:00 pm
Venue Name: En ligne/online