6 citations · 18 across the 7 of their papers we have counts for
10 papers
Ringel self-duality of hereditary algebras via Auslander-Reiten theory
Tiago Cruz
Highest weight categories with finitely many simples correspond to quasi-hereditary algebras. Ringel duality shows that, up to Morita equivalence, quasi-hereditary algebras come in…
Characteristic tilting modules and Ringel duality in the Noetherian world
Tiago Cruz
The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolv…
Higher Morita-Tachikawa correspondence
Tiago Cruz
Important correspondences in representation theory can be regarded as restrictions of the Morita--Tachikawa correspondence. Moreover, this correspondence motivates the study of man…
Quasi-hereditary covers of Temperley-Lieb algebras and relative dominant dimension
Tiago Cruz, Karin Erdmann
Many connections and dualities in representation theory can be explained using quasi-hereditary covers in the sense of Rouquier. The concepts of relative dominant and codominant di…
On split quasi-hereditary covers and Ringel duality
Tiago Cruz
In this paper, we develop two new homological invariants called relative dominant dimension with respect to a module and relative codominant dimension with respect to a module. The…
On Noetherian algebras, Schur functors and Hemmer-Nakano dimensions
Tiago Cruz
Important connections in representation theory arise from resolving a finite-dimensional algebra by an endomorphism algebra of a generator-cogenerator with finite global dimension;…
Cellular Noetherian algebras with finite global dimension are split quasi-hereditary
Tiago Cruz
We prove that cellular Noetherian algebras with finite global dimension are split quasi-hereditary over a regular commutative Noetherian ring with finite Krull dimension and their…
On properly stratified Gorenstein algebras
Tiago Cruz, René Marczinzik
We show that a properly stratified algebra is Gorenstein if and only if the characteristic tilting module coincides with the characteristic cotilting module. We further show that p…
Schur--Weyl duality over commutative rings
Tiago Cruz
The classical case of Schur--Weyl duality states that the actions of the group algebras of and on the -tensor power of a free module of finite rank centralize…
A characterisation of Morita algebras in terms of covers
Tiago Cruz
A pair is called a cover of if the Schur functor is fully faithful on the full subcategory of projective -mo…