arXiv subjects
Publications and source records attributed to Judith Marquardt.
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.
Let $A$ be a gentle algebra. For every collection of string and band diagrammes, we consider the constructible subset of the variety of representations containing all modules with this underlying diagramme. We study degenerations of such sets. We show that these sets are defined by vectors of integers which we call $h$-vectors and which are related to a restricted version of the hom-order. We provide combinatorial criteria for the existence of a degeneration, involving the removal of an arrow or the resolving of a type of configuration called "reaching".
We give a combinatorial classification of Nakayama algebras of small homological dimension using the Krattenthaler bijection between Dyck paths and 132-avoiding permutations.