On Matroids and Orlik-Solomon Algebras

被引：1
|
作者：
Yukihito Kawahara
机构：
[1] Tokyo Metropolitan University,Department of Mathematics
来源：
Annals of Combinatorics | 2004年 / 8卷 / 1期
关键词：
matroid; geometric lattice; geometric semilattice; Orlik-Solomon algebra; hyperplane arrangement;
D O I：
10.1007/s00026-004-0205-7
中图分类号：
学科分类号：
摘要：
In this paper we axiomatize combinatorics of arrangements of affine hyperplanes, which is a generalization of matroids, called quasi-matroids. We show that quasi-matroids are equivalent to pointed matroids. On the other hand, the Orlik-Solomon (OS) algebra of a quasimatroid can be constructed. We prove that the OS algebra of a quasi-matroid is isomorphic to the direct image of the OS algebra of a matroid by the linear derivation.
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页码：63 / 80
页数：17
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