CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

The Face Semigroup Algebra of a Hyperplane Arrangement

  Published:2009-08-01
 Printed: Aug 2009
  • Franco V. Saliola
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. It is shown that the algebra depends only on the intersection lattice of the hyperplane arrangement. A complete system of primitive orthogonal idempotents for the algebra is constructed and other algebraic structure is determined including: a description of the projective indecomposable modules, the Cartan invariants, projective resolutions of the simple modules, the Hochschild homology and cohomology, and the Koszul dual algebra. A new cohomology construction on posets is introduced, and it is shown that the face semigroup algebra is isomorphic to the cohomology algebra when this construction is applied to the intersection lattice of the hyperplane arrangement.
MSC Classifications: 52C35, 05E25, 16S37 show english descriptions Arrangements of points, flats, hyperplanes [See also 32S22]
Group actions on posets and homology groups of posets (See also 06A11)
Quadratic and Koszul algebras
52C35 - Arrangements of points, flats, hyperplanes [See also 32S22]
05E25 - Group actions on posets and homology groups of posets (See also 06A11)
16S37 - Quadratic and Koszul algebras
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/