The Face Semigroup Algebra of a Hyperplane Arrangement

Details The Face Semigroup Algebra of a Hyperplane Arrangement The Face Semigroup Algebra of a Hyperplane Arrangement

2005-11-29

arxiv.org/abs/math/0511717v2

Mathematics

Rings and Algebras

37 pages, LaTeX; Added section 8.3B; Changed the wording of a few paragraphs in the introduction and abstract. No major change

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Face Semigroup Algebra of a Hyperplane Arrangement does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Face Semigroup Algebra of a Hyperplane Arrangement, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Face Semigroup Algebra of a Hyperplane Arrangement will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-430034