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Noncommutative geometry in the sense of Connes and beyond: noncommutative algebras viewed as functions on a noncommutative space.

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Center of universal enveloping algebra of nilpotent lie algebra

Yes. Let $J(\mathfrak{g}) := (Z(\mathfrak{g}) \cap \mathfrak{g} U( \mathfrak{g} ) ) \cdot U(\mathfrak{g})$ denote the ideal of $U(\mathfrak{g})$ you're interested in. First note that if $\mathfrak{g} …
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