Representation dimension and finitely generated cohomology

Details Representation dimension and finitely generated cohomology Representation dimension and finitely generated cohomology

2007-11-18

arxiv.org/abs/0711.2794v1

Mathematics

Representation Theory

9 pages

Scientific paper

We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal complexity occurring among its modules. This provides a unified approach to computing lower bounds for the representation dimension of group algebras, exterior algebras and Artin complete intersections. We also obtain new examples of classes of algebras with arbitrarily large representation dimension.

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