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- Peter Jørgensen
- 2006

In a previous paper, Auslander-Reiten triangles and quivers were introduced into algebraic topology. This paper shows that over a Poincaré duality space, each component of the Auslander-Reiten quiver is isomorphic to ZA∞.

- Peter Jørgensen
- 2003

The homotopy category of complexes of projective left-modules over any reasonably nice ring is proved to be a compactly generated triangulated category, and a duality is given between its subcategory of compact objects and the finite derived category of right-modules.

We give a complete classification of torsion pairs in the cluster category of Dynkin type An. Along the way we give a new combinatorial description of Ptolemy diagrams, an infinite version of which was introduced by Ng (1005.4364v1 [math.RT], 2010). This allows us to count the number of torsion pairs in the cluster category of type An. We also count torsion… (More)

- Christine Bessenrodt, Thorsten Holm, Peter Jørgensen
- J. Comb. Theory, Ser. A
- 2014

Frieze patterns (in the sense of Conway and Coxeter) are in close connection to triangulations of polygons. Broline, Crowe and Isaacs have assigned a symmetric matrix to each polygon triangulation and computed the determinant. In this paper we consider d-angulations of polygons and generalize the combinatorial algorithm for computing the entries in the… (More)

Let k be a field and let D be a k-linear algebraic triangulated category with split idempotents. Let Σ be the suspension functor of D and let s be a 2-spherical object of D, that is, the morphism space D(s,Σs) is k for i = 0 and i = 2 and vanishes otherwise. Assume that s classically generates D, that is, each object of D can be built from s using… (More)

- Peter Jørgensen
- 2003

The main result of this paper is that over a noncommutative Koszul algebra, high truncations of finitely generated graded modules have linear free resolutions.

- Peter Jørgensen
- 2006

Differential Graded Algebras can be studied through their Differential Graded modules. Among these, the compact ones attract particular attention. This paper proves that over a suitable chain Differential Graded Algebra R, each compact Differential Graded module M satisfies ampM ≥ ampR, where amp denotes amplitude which is defined in a straightforward way… (More)

- Peter Jørgensen
- 2014

The (usual) Caldero-Chapoton map is a map from the set of objects of a category to a Laurent polynomial ring over the integers. In the case of a cluster category, it maps “reachable” indecomposable objects to the corresponding cluster variables in a cluster algebra. This formalises the idea that the cluster category is a “categorification” of the cluster… (More)

- Peter Jørgensen
- 2008

known as the left big finitistic projective dimension of A, is finite. Here pdM denotes the projective dimension of M . Unfortunately, this number is not known to be finite even if A is a finite dimensional algebra over a field, where, indeed, its finiteness is a celebrated conjecture. On the other hand, for such an algebra, finite flat certainly implies… (More)

- Peter Jørgensen, Lidija Milković, Neven Zarkovic, Georg Waeg, Suresh I. S. Rattan
- Biogerontology
- 2013

The reactive aldehyde, 4-hydroxynonenal (HNE), is recognized as a product of lipid peroxidation, which binds to macromolecules, in particular proteins. HNE-modified proteins (HNE-MP) have been shown to accumulate during ageing, generally by using polyclonal antibodies, which increase the possibility of detecting false positives. Therefore, we have used a… (More)