A Deformation of the Orlik-Solomon Algebra

• Autores: István Heckenberger, Volkmar Welker
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 118, Nº 2, 2016, págs. 183-202
• Idioma: inglés
• DOI: 10.7146/math.scand.a-23686
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• Resumen

  • A deformation of the Orlik-Solomon algebra of a matroid $\mathfrak{M}$ 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 Gröbner 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 Gröbner basis and hence the algebra is Koszul.