THE INGALLS-THOMAS BIJECTIONS

Abstract

Given a finite acyclic quiver Q with path algebra Λ, Ingalls and Thomas have exhibited a bijection between the set of Morita equivalence classes of support-tilting modules and the set of thick subcategories of mod Λ with covers, and they have collected further bijections with these sets. We add some additional bijections and show that all these bijections hold for arbitrary hereditary artin algebras. The proofs presented here seem to be of interest also in the special case of the path algebra of a quiver

Keywords

• Tilting module, support-tilting module, thick subcategory, normal module, conormal module, torsion pair, antichain, exceptional antichain