The rigid dualizing complex of a universal enveloping algebra

Amnon Yekutieli

doi:10.1016/S0022-4049(99)00032-8

The rigid dualizing complex of a universal enveloping algebra

Amnon Yekutieli

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

30 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 language	English
Pages (from-to)	85-93
Number of pages	9
Journal	Journal of Pure and Applied Algebra
Volume	150
Issue number	1
DOIs	https://doi.org/10.1016/S0022-4049(99)00032-8
State	Published - 14 Jun 2000

ASJC Scopus subject areas

Algebra and Number Theory

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AB - 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.

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The rigid dualizing complex of a universal enveloping algebra

Abstract

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