**Publication status:** *J. Pure Appl. Algebra* ** 150
** (2000), no. 1, 85--93.

**Eprint **(at http://xxx.lanl.gov): math.RA/9810016

**Abstract:**

Let k be a field and A a noetherian (noncommutative) k-algebra.

The rigid dualizing complex of A was introduced by Van den Bergh.

When A = U(g), the enveloping algebra of a finite dimensional Lie

algebra g, Van den Bergh conjectured that the rigid dualizing complex

is (U(g) \otimes \wedge^{n} g )[n], where n = dim g. We prove this

conjecture, and give a few applications in representation theory and

Hochschild cohomology.

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(updated 11.6.02)