Homological properties of Orlik-Solomon algebras
Autor(en): | Kaempf, Gesa Roemer, Tim |
Stichwörter: | COHOMOLOGY; EXTERIOR; FREE RESOLUTIONS; Mathematics | Erscheinungsdatum: | 2009 | Herausgeber: | SPRINGER HEIDELBERG | Enthalten in: | MANUSCRIPTA MATHEMATICA | Band: | 129 | Ausgabe: | 2 | Startseite: | 181 | Seitenende: | 210 | Zusammenfassung: | 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. |
ISSN: | 00252611 | DOI: | 10.1007/s00229-009-0254-7 |
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geprüft am 06.06.2024