Combinatorial and Algebraic Structure in Orlik-Solomon Algebras

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)687-698
Number of pages12
JournalEuropean Journal of Combinatorics
Volume22
Issue number5
DOIs
StatePublished - Jul 2001

Fingerprint

Matroid
Algebraic Structure
Algebra
Isomorphism theorems
Exterior Algebra
Hyperplane Arrangement
Invariant
Free Algebras
Categorical
Homotopy
Modulo
Open Problems
Complement
Theorem
Networks (circuits)
Framework

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Combinatorial and Algebraic Structure in Orlik-Solomon Algebras. / Falk, Michael J.

In: European Journal of Combinatorics, Vol. 22, No. 5, 07.2001, p. 687-698.

Research output: Contribution to journalArticle

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