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Orlik–Solomon Type Algebras

✍ Scribed by David Forge; Michel Las Vergnas

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
92 KB
Volume
22
Category
Article
ISSN
0195-6698

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✦ Synopsis

We introduce χ-algebras, and show that a χ-algebra has the NBC basis property. We also show that a certain ideal used in the construction has the so-called BC basis property. The Orlik-Solomon algebra of a matroid, the Orlik-Terao algebra of a set of vectors, and the Cordovil algebra of an oriented matroid are χ-algebras. We define a new χ -algebra from a set of vectors, close to the Orlik-Terao, Orlik-Terao, and Cordovil algebras, but nevertheless different. Our proof provides a unified short and elementary proof of the NBC basis property for these algebras.

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