Bases in Orlik-Solomon Type Algebras

The Orlik-Solomon algebra of a matroid M is the quotient of the exterior algebra on the points by the ideal (M) generated by the boundaries of the circuits of the matroid. There is an isomorphism between the Orlik-Solomon algebra of a complex matroid and the cohomology of the complement of a complex arrangement of hyperplanes. In this article a generalization of the Orlik-Solomon algebras, called -algebras, are considered. These new algebras include, apart from the Orlik-Solomon algebras, the Orlik-Solomon-Terao algebra of a set of vectors and the Cordovil algebra of an oriented matroid. To encode an important property of the "no broken circuit bases" of the Orlik-Solomon-Terao algebras, Andr

• Type: Journal
• Year: 2002
• Where: EJC
• Authors: David Forge
• Keywords: Algebras, EJC 2002, Information Technology, Matroid, Orlik-solomon Algebras