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

K. De Naeghel·N. Marconnet
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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.

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K. De Naeghel, N. Marconnet. 2006-01-05. Ideals of cubic algebras and an invariant ring of the Weyl algebra. https://arxiv.org/abs/math/0601096

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