Bijection between strong torsion classes and maximal support pre-tilting modules
Bijection between strong torsion classes and maximal support pre-tilting modules
Let be an almost-directed -homological pair, meaning that is an algebra equipped with the subcategory , and suppose that
A -strong torsion class in is a torsion class satisfying the stated -strongness condition, and a maximal support pre--tilting -module is a support pre--tilting module maximal with respect to the relevant inclusion. The bijection conjecture. There is a bijection between -strong torsion classes in and maximal support pre--tilting -modules. This conjecture would classify -strong torsion classes in , extending the preceding theorem's construction from proper support--tilting modules to all maximal support pre--tilting modules. The supplied text gives no resolution, so the conjecture remains open.
Sources & referencesView supporting material
Primary source
Jordan McMahon, “Higher support tilting I: higher Auslander algebras of linearly oriented type A”, arXiv:1808.05184 (2018).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.