A deformation of the Orlik-Solomon algebra

Details A deformation of the Orlik-Solomon algebra A deformation of the Orlik-Solomon algebra

2011-09-09

arxiv.org/abs/1109.1945v1

Mathematics

Combinatorics

Scientific paper

A deformation of the Orlik-Solomon algebra of a matroid M is defined as a quotient of the free associative algebra over a commutative ring R with 1. It is shown that the given generators form a Groebner basis and that after suitable homogenization the deformation and the Orlik-Solomon have the same Hilbert series as R-algebras. For supersolvable matroids, equivalently fiber type arrangements, there is a quadratic Groebner basis and hence the algebra is Koszul

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