On some properties of LS algebras
arXiv:1809.10191 · doi:10.1142/S0219199718500852
Abstract
The discrete LS algebra over a totally ordered set is the homogeneous coordinate ring of an irreducible projective (normal) toric variety. We prove that this algebra is the ring of invariants of a finite abelian group containing no pseudo-reflection acting on a polynomial ring. This is used to study the Gorenstein property for LS algebras. Further we show that any LS algebra is Koszul.
11 pages, minor editing in references, accepted by Communications in Contemporary Mathematics