A new characterisation of Auslander-Gorenstein algebras
Viktória Klász, Markus Kleinau, Rene Marczinzik, Judith Marquardt
Abstract
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-Reiten bijection. This proves a conjecture of Marczinzik. We use this to give a new proof that a finite lattice with an Auslander-Gorenstein incidence algebra has to be distributive.
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