Auslander-Reiten theory for simply connected differential graded algebras

Details Auslander-Reiten theory for simply connected differential graded algebras Auslander-Reiten theory for simply connected differential graded algebras

2008-01-04

arxiv.org/abs/0801.0651v1

Mathematics

Representation Theory

58 pages, doctoral thesis University of Paderborn (2007)

Scientific paper

Peter Jorgensen introduced the Auslander-Reiten quiver of a simply connected Poincare duality space. He showed that its components are of the form ZA_infty and that the Auslander-Reiten quiver of a d-dimensional sphere consists of d-1 such components. In this thesis we show that this is the only case where finitely many components appear. More precisely, we construct families of modules, where for each family, each module lies in a different component. Depending on the cohomology dimensions of the differential graded algebras which appear, this is either a discrete family or an n-parameter family for all n.

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