Bernt Tore Jensen

A categorification of Grassmannian cluster algebras

We describe a ring whose category of Cohen-Macaulay modules provides an additive categorication the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of k-planes in n-space. More precisely, there is a cluster character dened on the category which maps the rigid indecomposable objects to the cluster variables and the maximal rigid objects to clusters. This is proved by showing that the quotient of this category by a single projective-injective object is Geiss-Leclerc-Schroers category Sub Qk, which categories the coordinate ring of the big cell in this Grassmannian.

DEGENERATION-LIKE ORDERS IN TRIANGULATED CATEGORIES

In an earlier paper we defined a relation ≤Δ between objects of the derived category of bounded complexes of modules over a finite dimensional algebra over an algebraically closed field. This relation was shown to be equivalent to the topologically defined degeneration order in a certain space for derived categories. This space was defined as a natural generalization of varieties for modules. We remark that this relation ≤Δ is defined for any triangulated category and show that under some finiteness assumptions on the triangulated category ≤Δ is always a partial order.

DEGENERATION OF A-INFINITY MODULES

In this paper we use A∞-modules to study the derived cat- egory of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A∞-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasi- isomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of Zwara and Riedt- mann for modules.

Filtrations in Abelian categories with a tilting object of homological dimension two

We consider filtrations of objects in an abelian category

Varieties of complexes of fixed rank

\catA

Rigid representations of a double quiver of type A, and Richardson elements in seaweed Lie algebras

induced by a tilting object

A category for Grassmannian cluster algebras

T

A geometric realisation of 0-Schur and 0-Hecke algebras

of homological dimension at most two. We define three disjoint subcategories with no maps between them in one direction, such that each object has a unique filtation with factors in these categories. This filtration coincides with the the classical two-step filtration induced by torsion pairs in dimension one. We also give a refined filtration, using the derived equivalence between the derived categories of

Projective modules of 0-Schur algebras

\catA

Adjoint Action of Automorphism Groups on Radical Endomorphisms, Generic Equivalence and Dynkin Quivers

and the module category of