✦ LIBER ✦
Line-Closed Matroids, Quadratic Algebras, and Formal Arrangments
✍ Scribed by Michael Falk
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 159 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0196-8858
No coin nor oath required. For personal study only.
✦ Synopsis
Let G be a matroid on ground set . The Orlik-Solomon algebra A G is the quotient of the exterior algebra on by the ideal generated by circuit boundaries. The quadratic closure A G of A G is the quotient of by the ideal generated by the degree-two component of . We introduce the notion of the nbb set in G, determined by a linear order on , and show that the corresponding monomials are linearly independent in the quadratic closure A G . As a consequence, A G is a quadratic algebra only if G is line-closed. An example of S. Yuzvinsky proves the converse false. [G.