JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (06): 89-94.doi: 10.6040/j.issn.1671-9352.0.2015.080

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Quadratic Gröbner basis and the isomorphism of Orlik-Solomon algebras

GAO Rui-mei, SUN Yan   

  1. School of Science, Changchun University of Science and Technology, Changchun 130022, Jilin, China
  • Received:2015-02-27 Revised:2015-05-20 Online:2015-06-20 Published:2015-07-31

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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 Gröbner 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 Gröbner 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.

Key words: the quadratic arrangement, the quadratic Grö, isomorphism, bner basis, framing, Orlik-Solomon algebra

CLC Number: 

  • O189
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