Ideals of cubic algebras and an invariant ring of the Weyl algebra

2006/01/05 by De Naeghel, K., Marconnet, N.
#16D25 #16S38 #18E30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.math/0601096

Abstract

We classify reflexive graded right ideals, up to isomorphism and shift, of generic cubic three dimensional Artin-Schelter regular algebras. We also determine the possible Hilbert functions of these ideals. These results are obtained by using similar methods as for quadratic Artin-Schelter algebras. In particular our results apply to the enveloping algebra of the Heisenberg-Lie algebra from which we deduce a classification of right ideals of an invariant ring of the first Weyl algebra.

Related

• Ideal classes of three dimensional Sklyanin algebras
• Ideal classes of three dimensional Artin-Schelter regular algebras
• Classification of quadratic and cubic PBW algebras on three generators
• Symmetric Ideals and Invariant Hilbert Schemes
• Hilbert series of modules of GK-dimension two over elliptic algebras