arXiv math/00101682000-10-17math.COmath.RA

Annihilators of Ideals of Exterior Algebras

Graham Denham, Sergey Yuzvinsky

备注：: 18 pages; submitted to Advances in Applied Math

英文摘要：

The Orlik-Solomon algebra A of a matroid is isomorphic to the quotient of an exterior algebra E by a defining ideal I. We find an explicit presentation of the annihilator ideal of I or, equivalently, the E-module dual to A. As an application of that we provide a necessary, combinatorial condition for the algebra A to be quadratic. We show that this is stronger than matroid being line-closed thereby resolving (negatively) a conjecture by Falk. We also show that our condition is not sufficient for the quadraticity.

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