二次Grbner基及Orlik-Solomon代数同构  

Quadratic Grbner basis and the isomorphism of Orlik-Solomon algebras

作　　者：高瑞梅[1] 孙艳[1] 

机构地区：[1]长春理工大学理学院,吉林长春130022

出　　处：《山东大学学报（理学版）》2015年第6期89-94,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11326078);长春理工大学科技创新基金项目(XJJLG-2014-01)

摘　　要：Orlik-Solomon代数是基于构形A的外代数E模去一个齐次理想I的商代数。研究了二次构形与二次Grbner基之间的关系,得到了中心构形A是一个二次构形当且仅当I具有二次Grbner基,给出了直接证明。对于构形的Orlik-Solomon代数,分别针对中心构形和仿射构形给出了其最高次分支的同构定理。The Orlik-Solomon algebra is the quotient of the exterior algebra E based on A by a homogeneous ideal I. The relations between a quadratic arrangement and a quadratic Gr6bner basis are studied. And the proof of the conclusion that a central arrangement is a quadratic arrangement if and only if I has a quadratic Grobner basis is given. We do some research on the Orlik-Solomon algebras for central and affine arrangements, and give the isomorphism theorems for the top dimensional parts of Orlik-Solomon algebras.

关 键 词：二次构形 二次Grobner基 Orlik-Solomon代数 标架 同构 

分 类 号：O189[理学—数学]