The rigid dualizing complex of a universal enveloping algebra

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26 Scopus citations

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)⊗ ∧n g)[n] where n=dim g. We prove this conjecture, and give a few applications in representation theory and Hochschild cohomology.

Original languageEnglish
Pages (from-to)85-93
Number of pages9
JournalJournal of Pure and Applied Algebra
Volume150
Issue number1
DOIs
StatePublished - 14 Jun 2000

ASJC Scopus subject areas

  • Algebra and Number Theory

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