Combinatorial and algebraic structure in OrlikSolomon algebras
Abstract
The OrlikSolomon algebra ${\cal A}(G)$ of a matroid $G$ is the free exterior algebra on the points, modulo the ideal generated by the circuit boundaries. On one hand, this algebra is a homotopy invariant of the complement of any complex hyperplane arrangement realizing $G$. On the other hand, some features of the matroid $G$ are reflected in the algebraic structure of ${\cal A}(G)$. In this mostly expository article, we describe recent developments in the construction of algebraic invariants of ${\cal A}(G)$. We develop a categorical framework for the statement and proof of recently discovered isomorphism theorems which suggests a possible setting for classification theorems. Several specific open problems are formulated.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2000
 arXiv:
 arXiv:math/0009135
 Bibcode:
 2000math......9135F
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Rings and Algebras;
 52C35;
 05B35
 EPrint:
 16 pages, 1 figure. to appear in European J. Combinatorics Special Issue  Proceedings of OM99 at CIRM