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Faithful Cyclic Modules for Enveloping Algebras and Sklyanin Algebras

Ian M. Musson
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Abstract

Let $U$ be the enveloping algebra of a finite dimensional nonabelian Lie algebra $\mathfrak{g}$ over a field of characteristic zero. We show that there is an open nonempty open subset $X$ of $U_1 = \mathfrak{g}\oplus K$ such that $U/Ux$ is faithful for all $x \in X$. 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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BibTeXRIS

Ian M. Musson. 2005-10-12. Faithful Cyclic Modules for Enveloping Algebras and Sklyanin Algebras. https://arxiv.org/abs/math/0510262

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