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ON THE ORLIK-SOLOMON ALGEBRA OF A HYPERSOLVABLE ARRANGEMENT | ||
| Journal of Basrah Researches (Sciences) | ||
| Article 1, Volume 36, Issue 1, 2010, Pages 19-43 PDF (0 K) | ||
| Authors | ||
| Abd Ali Al-Ta; ; M. Aliand Mayadah A. Majeed | ||
| Abstract | ||
| This paper is devoted to construct the Orlik-Solomon algebra of a hypersolvable -arrangement by using the hypersolvable partition analogue. We used the hypersolvable ordering which preserves the hypersolvable structure to define the NBC-basis of the Orlik-Solomon algebra and we embedded it in the partition module as a free graded submodule. We used this ordering also to prove that a hypersolvable arrangement is quadratic if, and only if, it's fiber-type. As a generalization of a result of Jambu and Papadima, we gave the quadratic Orlik-Solomon algebra a structure isomorphic to a partition module and we used this isomorphism to produce a comparison between the Orlik-Solomon algebra and the quadratic Orlik-Solomon algebra as free modules with many applications. | ||
| Keywords | ||
| Hyperplane arrangements; hypersolvable arrangements; the exterior algebra | ||
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