3 papers
math.RT2025
A new formula for the classical dominant dimension using bimodules
Tiago Cruz, René Marczinzik
We show that a faithful projective-injective module over a finite-dimensional algebra has the double centraliser property if and only if as a bimodule is reflexive. More ge…
math.RT2025
An Auslander-Buchsbaum formula for higher Auslander algebras and applications
Tiago Cruz, René Marczinzik
We provide a new non-commutative generalisation of the Auslander-Buchsbaum formula for higher Auslander algebras and use this to show that the class of tilted Auslander algebras, s…
math.RT2024
Higher torsion-free Auslander-Reiten sequences and the dominant dimension of algebras
Tiago Cruz, René Marczinzik
We generalise a theorem of Tachikawa about reflexive Auslander-Reiten sequences. We apply this to give a new characterisation of the dominant dimension of gendo-symmetric algebras.…