Annihilators of Orlik–Solomon Relations

✍ Scribed by Graham Denham; Sergey Yuzvinsky

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 163 KB
• Volume: 28
• Category: Article
• ISSN: 0196-8858
• DOI: 10.1006/aama.2001.0779

✦ Synopsis

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 the matroid being line-closed, thereby resolving (negatively) a conjecture by M. Falk. We also show that our condition is not sufficient for quadraticity.  2002 Elsevier Science (USA)