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.
23 October Friday
Eric Hanson (Brandeis): Canonical join and meet representations in lattices of torsion classes
23 October 2020, 11:00 - 23 October 2020, 12:00
En ligne/online, Canada