Artin-Schelter regular algebras of dimension five
arXiv:0911.5129
Abstract
We show that there are exactly three types of Hilbert series of Artin-Schelter regular algebras of dimension five with two generators. One of these cases (the most extreme) may not be realized by an enveloping algebra of a graded Lie algebra. This is a new phenomenon compared to lower dimensions, where all resolution types may be realized by such enveloping algebras.
23 pages, added a section with a direct proof that the universal enveloping algebra of a finite dimensional positively graded Lie algebra is Artin-Schelter regular