Séminaires : Séminaire d'Algèbre

A famous result in representation theory is Auslander’s correspondence which connects finite-dimensional algebras of finite representation-type with Auslander algebras. Over the years, many generalisations of Auslander algebras have been proposed: for instance n-Auslander algebras (by Iyama), n-minimal Auslander–Gorenstein algebras (by Iyama and Solberg), among others. All of the concepts above require the existence of a faithful projective-injective module and use classical dominant dimension. Now replace the faithful projective-injective module with a self-orthogonal module and classical dominant dimension with relative dominant dimension with respect to a module and you get a relative Auslander-Gorenstein pair.

In this talk, we introduce relative Auslander-Gorenstein pairs. Further, we will characterise relative Auslander pairs (those whose underlying algebras have finite global dimension) by the existence and uniqueness of tilting-cotilting modules having the highest values of relative dominant and codominant dimension with respect to the self-orthogonal module. At the end, we discuss explicit examples of relative Auslander pairs. (This is joint work with Chrysostomos Psaroudakis.)

This talk will take place in hybrid mode at the Institut Henri Poincaré.