Title: The Rigid Dualizing Complex of a Universal Enveloping Algebra

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

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

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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