✦ LIBER ✦

Bases in Orlik–Solomon Type Algebras

✍ Scribed by David Forge

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 85 KB
Volume: 23
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2002.0580

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✦ Synopsis

Let M be a matroid on [n] and E be the graded algebra generated over a field k generated by the elements 1, e 1 , . . . , e n . Let (M) be the ideal of E generated by the squares e 2 1 , . . . , e 2 n , elements of the form e i e j + a i j e j e i and 'boundaries of circuits', i.e., elements of the form χ j e i 1 . . . e i j-1 e i j+1 . . . e i m , with χ j ∈ k and e i 1 , . . . , e i m a circuit of the matroid with some special coefficients. The χ -algebra A(M) is defined as the quotient of E by (M). Recall that the class of χ -algebras contains several studied algebras and in first place the Orlik-Solomon algebra of a matroid. We will essentially construct the reduced Gröbner basis of (M) for any term order and give some consequences.

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