13 papers · 1 filter
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…
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…
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…
Total preprojective algebras
Aaron Chan, Osamu Iyama, Rene Marczinzik
We introduce total preprojective algebras of path algebras of Dynkin quivers , and prove that they are isomorphic to -Auslander algebras of preprojective algebras …