Combinatorial and Algebraic Structure in Orlik-Solomon Algebras
Combinatorial and Algebraic Structure in Orlik-Solomon Algebras
复制标题
Orlik-Solomon 代数中的组合和代数结构
DOI：
10.1006/eujc.2000.0488
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
M. Falk
中科院分区：
文献类型：
--
作者：
M. Falk
奥力克？拟阵G的所罗门代数A（G）是点上的自由外代数，模由回路边界生成的理想。一方面，该代数是实现G的任何复超平面排列的补的同伦不变量;另一方面，拟阵G的一些特征也反映在A（G）的代数结构中。在这篇文章中，我们描述了最近的发展，在建设的代数不变量A（G）。我们开发了一个分类框架的声明和证明最近发现的同构定理，这表明一个可能的设置分类定理。几个具体的开放问题制定。
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.