1. CJM 2009 (vol 61 pp. 904)
||The Face Semigroup Algebra of a Hyperplane Arrangement |
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.
Categories:52C35, 05E25, 16S37