A Commutative Algebra for Oriented Matroids

Let V be a vector space of dimension d over a field K and let A be a central arrangement of hyperplanes in V. To answer a question posed by K. Aomoto, P. Orlik and H. Terao construct a commutative K-algebra U(A) in terms of the equations for the hyperplanes of A. In the course of their work the following question naturally occurred: Is U(A) determined by the intersection lattice L(A) of the hyperplanes of A? We give a negative answer to this question. The theory of oriented matroids gives rise to a combinatorial analogue of the algebra of Orlik

• Type: Journal
• Year: 2002
• Where: DCG
• Authors: Raul Cordovil
• Keywords: Central Arrangement, Commutative K-algebra, DCG 2002, Vector Space