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arXiv · 0803.0064

Homological properties of Orlik-Solomon algebras

Gesa Kaempf·Tim Roemer
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Abstract

The Orlik-Solomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E. At first we study homological properties of E-modules as e.g. complexity, depth and regularity. In particular, we consider modules with linear injective resolutions. We apply our results to Orlik-Solomon algebras of matroids and give formulas for the complexity, depth and regularity of such rings in terms of invariants of the matroid. Moreover, we characterize those matroids whose Orlik-Solomon ideal has a linear projective resolution and compute in these cases the Betti numbers of the ideal.

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BibTeXRIS

Gesa Kaempf, Tim Roemer. 2008-03-01. Homological properties of Orlik-Solomon algebras. https://doi.org/10.1007/s00229-009-0254-7

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