Markus Kleinau

collaborators

5 papers

math.RT2026

A new characterisation of Auslander-Gorenstein algebras

ViktÃ³ria KlÃ¡sz, 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…

math.RT2026

Classification of Auslander-Gorenstein monomial algebras: The acyclic case

ViktÃ³ria KlÃ¡sz, Markus Kleinau, RenÃ© 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…

math.RT2026

Cambrian lattices are fractionally Calabi-Yau via 2-cluster combinatorics

Markus Kleinau

Reading constructed a Cambrian lattice $C_{I^} $ for each oriented finite type Coxeter diagram $I^$ . We show that the derived category of representations of $C_{I^} $ is fractionally Cal…

math.RT2025

Pure minimal injective resolutions and perfect modules for lattices

Tal Gottesman, ViktÃ³ria KlÃ¡sz, 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…

math.RT2025

Scalar extensions of quiver representations over $F_{1}$

Markus Kleinau

Let $V$ and $W$ be quiver representations over $F_{1}$ and let $K$ be a field. The scalar extensions $V^{K}$ and $W^{K}$ are quiver representations over $K$ with a distinguished…

A new characterisation of Auslander-Gorenstein algebras

Classification of Auslander-Gorenstein monomial algebras: The acyclic case

Cambrian lattices are fractionally Calabi-Yau via 2-cluster combinatorics

Pure minimal injective resolutions and perfect modules for lattices

Scalar extensions of quiver representations over F1​

Scalar extensions of quiver representations over $F_{1}$