7 papers
A new characterisation of Auslander-Gorenstein algebras
Viktória Klász, Viktória Klász, Markus Kleinau +2
We give a new characterisation of Auslander-Gorenstein finite dimensional algebras by showing that they are exactly the finite dimensional algebras with a well-defined Auslander-Re…
Classification of Auslander-Gorenstein monomial algebras: The acyclic case
Viktória Klász, Markus Kleinau, René Marczinzik
We give a linear algebraic classification of Auslander regular acyclic monomial algebras via the Bruhat factorisation of the Coxeter matrix. Namely, we show under mild assumptions…
Pure minimal injective resolutions and perfect modules for lattices
Tal Gottesman, Viktória Klász, Markus Kleinau +1
In a recent article, Iyama and Marczinzik showed that a lattice is distributive if and only if the incidence algebra is Auslander regular, giving a new connection between homologic…
A survey on Auslander-Gorenstein algebras
Viktória Klász, Rene Marczinzik
We give a survey on Auslander-Gorenstein algebras with a focus on finite-dimensional algebras. We put an emphasis on recent classification results for special classes of algebras a…
The Auslander-Gorenstein condition for monomial algebras
Viktória Klász
This paper investigates the Auslander-Gorenstein property for monomial algebras. First, we prove that every Auslander-Gorenstein monomial algebra is a string algebra and present a…
On the global dimension of Nakayama algebras
Viktória Klász, René Marczinzik, Anton Mellit +2
We study the global dimension of Nakayama algebras. In the case of linear Nakayama algebras, which are in canonical bijection to Dyck paths, we show that the global dimension has t…