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Combinatorial and Algebraic Structure in Orlik–Solomon Algebras

✍ Scribed by Michael Falk

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
188 KB
Volume
22
Category
Article
ISSN
0195-6698

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✦ Synopsis

The Orlik-Solomon algebra 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 A(G).

In this mostly expository article, we describe recent developments in the construction of algebraic invariants of 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.

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