TY - JOUR
T1 - Combinatorial and Algebraic Structure in Orlik-Solomon Algebras
AU - Falk, Michael
N1 - Funding Information:
I am grateful to Raul Cordovil and Michel Las Vergnas for inviting me to speak at the CIRM conference, and for providing financial support. I thank Sergey Yuzvinsky for his help in studying quadratic O S algebras, and Alex Suciu for his suggestion to include resonance varieties over Zp, and his help in understanding them. My REU students Carrie Eschenbrenner, Cayley Pendergrass, and Samantha Melcher assisted me in sorting out much of the material in the last two sections. Finally I wish to thank Diane MacLagan for a helpful correspondence concerning Gröbner bases.
PY - 2001/7
Y1 - 2001/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0035618449&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035618449&partnerID=8YFLogxK
U2 - 10.1006/eujc.2000.0488
DO - 10.1006/eujc.2000.0488
M3 - Article
AN - SCOPUS:0035618449
SN - 0195-6698
VL - 22
SP - 687
EP - 698
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 5
ER -