Faithful Cyclic Modules for Enveloping Algebras and Sklyanin Algebras

2005/10/12 by Musson, Ian M.
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.math/0510262

Abstract

Let U be the enveloping algebra of a finite dimensional nonabelian Lie algebra \mathfrakg over a field of characteristic zero. We show that there is an open nonempty open subset X of U₁ = \mathfrakg⊕ K such that U/Ux is faithful for all x ∈ X. We prove similar results for homogenized enveloping algebras and for the three dimensional Sklyanin algebras at points of infinite order. It would be interesting to know if there is a common generalization of these results.

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