Dag Oskar Madsen

Hochschild homology and global dimension

We prove that for certain classes of graded algebras (Koszul, local, cellular), infinite global dimension implies that Hochschild homology does not vanish in high degrees, provided the characteristic of the ground field is zero. Our proof uses Igusas formula relating the Euler characteristic of relative cyclic homology to the graded Cartan determinant.

Hochschild homology and truncated cycles

We study algebras having 2-truncated cycles and show that these algebras have infinitely many nonzero Hochschild homology groups. Consequently, algebras of finite global dimension have no 2-truncated cycles and therefore satisfy a higher version of the “no loops conjecture”.

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

FINITE HOCHSCHILD COHOMOLOGY WITHOUT FINITE GLOBAL DIMENSION

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On a common generalization of Koszul duality and tilting equivalence

induced by a tilting object

Ext-algebras and derived equivalences

T

Quasi-hereditary algebras and generalized Koszul duality

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

On Auslander-Reiten translates in functorially finite subcategories and applications

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Hochschild homology and split pairs

and the module category of