18 papers
Tor and Ext vanishing results for commutative Artinian rings
Bernhard Böhmler, Rene Marczinzik
We give a negative answer to a question of Avramov, Buchweitz and Şega by constructing a commutative local finite-dimensional non-Gorenstein algebra with $\operatorname{Ext}_R^…
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…
Preprojective algebras and generalisations: A short survey
Aaron Chan, Osamu Iyama, Rene Marczinzik
The preprojective algebra of a hereditary algebra can be defined as a certain orbit construction of the regular representation generated by the Auslander-Reiten translation. In…
Spherical modules and the Auslander--Gorenstein condition for Auslander--Yoneda algebras
Finn Bauwens, Norihiro Hanihara, René Marczinzik +2
For a finite dimensional algebra of finite global dimension we study the Auslander--Yoneda algebra defined as the Yoneda algebra of the direct sum of all indecomposable -mod…
Benchmarks in Leipzig
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg +45
Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the 3…
Fractionally Calabi-Yau algebras and cluster tilting
Aaron Chan, Osamu Iyama, Rene Marczinzik
We show that the class of twisted fractionally Calabi-Yau algebras of finite global dimension coincides with the stable endomorphism algebras of -cluster tilting modules over $d…