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- 2015
二次Gr？bner基及Orlik-Solomon代数同构
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Abstract:
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。
Abstract: 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 Gr？bner 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 Gr？bner 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
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