Dirac Cohomology for the Cubic Dirac Operator

By B. Kostant. 2002

70 citations recorded by the source corpus.

Let \( \mathfrak{g} \) be a complex semisimple Lie algebra and let \( \mathfrak{r} \subset \mathfrak{g} \) be any reductive Lie subalgebra such that B∣ \( \mathfrak{r} \) is nonsingular where B is the Killing form of \( \mathfrak{g} \) . Let Z(r) and Z(g) be, respectively, the centers of the enveloping algebras of \( \mathfrak{r} \) and \( \mathfrak{r} \subset \mathfrak{g} \) . Using a Harish-Chandra isomorphism one has a homomorphism \( \eta :Z(\mathfrak{g}) \to Z(\mathfrak{r}) \) which, by a well-known result of H. Cartan, yields the the relative Lie algebra cohomology H(\( (\mathfrak{g},\mathfrak{r}) \).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4911ea613ec3bbba57f2ee42d1a434a780c80ff8

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Citations in the corpus

Dirac Operators in Representation Theory (2006, methodology): “This was proved in [K3], by constructing a sufficiently large family of highest weight modules with known infinitesimal characters and nonzero Dirac cohomology.”