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Algebras Related to Matroids Represented in Characteristic Zero

โœ Scribed by David G. Wagner

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
188 KB
Volume
20
Category
Article
ISSN
0195-6698

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โœฆ Synopsis

Let k be a field of characteristic zero. We consider graded subalgebras A of k[x 1 , . . . , x m ]/ (x 2 1 , . . . , x 2 m ) generated by d linearly independent linear forms. Representations of matroids over k provide a natural description of the structure of these algebras. In return, the numerical properties of the Hilbert function of A yield some information about the Tutte polynomial of the corresponding matroid. Isomorphism classes of these algebras correspond to equivalence classes of hyperplane arrangements under the action of the general linear group.

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