7 papers · 1 filter
A new characterisation of Auslander-Gorenstein algebras
Viktória Klász, Markus Kleinau, Rene Marczinzik +1
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…
Auslander regular algebras and Coxeter matrices
Viktória Klász, Rene Marczinzik, Hugh Thomas
We show that Iyama's grade bijection for Auslander-Gorenstein algebras coincides with the bijection introduced by Auslander-Reiten. This result uses a new characterisation of Ausla…
Nakayama algebras of small homological dimension and pattern avoiding permutations
Viktória Klász, René Marczinzik, Judith Marquardt
We give a combinatorial classification of Nakayama algebras of small homological dimension using the Krattenthaler bijection between Dyck paths and 132-avoiding permutations.