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Homological properties of Orlik–Solomon algebras

✍ Scribed by Gesa Kämpf; Tim Römer

Publisher
Springer
Year
2009
Tongue
English
Weight
334 KB
Volume
129
Category
Article
ISSN
0025-2611

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Orlik–Solomon Type Algebras
Orlik–Solomon Type Algebras
✍ David Forge; Michel Las Vergnas 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 92 KB

We introduce χ-algebras, and show that a χ-algebra has the NBC basis property. We also show that a certain ideal used in the construction has the so-called BC basis property. The Orlik-Solomon algebra of a matroid, the Orlik-Terao algebra of a set of vectors, and the Cordovil algebra of an oriented

Bases in Orlik–Solomon Type Algebras
Bases in Orlik–Solomon Type Algebras
✍ David Forge 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 85 KB

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

Combinatorial and Algebraic Structure in
Combinatorial and Algebraic Structure in Orlik–Solomon Algebras
✍ Michael Falk 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 188 KB

The Orlik-Solomon algebra A(G) of a matroid G is the free exterior algebra on the points, modulo the ideal generated by the circuit boundaries. On one hand, this algebra is a homotopy invariant of the complement of any complex hyperplane arrangement realizing G. On the other hand, some features of t

A Note on the Orlik–Solomon Algebra
A Note on the Orlik–Solomon Algebra
✍ Raul Cordovil; Gwihen Etienne 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 112 KB

Let M = M(E) be a matroid on a linear ordered set E. The Orlik-Solomon Z-algebra OS(M) of M is the free exterior Z-algebra on E, modulo the ideal generated by the circuit boundaries. The Z-module OS(M) has a canonical basis called 'no broken circuit basis' and denoted nbc. Let e X = e i , e i ∈ X ⊂