2008/12/07 by José Miguel Figueroa-O'Farrill · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #hep-th #math.DG #math.RT
paper · pdf · doi:10.1088/1742-6596/175/1/012002
published as J.Phys.Conf.Ser.175:012002,2009 · 16 pages
arxiv created 2008/12/07 · openalex publication_date 2009/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
These notes record three lectures given at the workshop "Higher symmetries in Physics", held at the Universidad Complutense de Madrid in November 2008. In them we explain how to construct a Lie (super)algebra associated to a spin manifold, perhaps with extra geometric data, and a notion of privileged spinors. The typical examples are supersymmetric supergravity backgrounds; although there are more classical instances of this construction. We focus on two results: the geometric constructions of compact real forms of the simple Lie algebras of type B 4 , F 4 and E 8 from S 7 , S 8 and S 15 , respectively; and the construction of the Killing superalgebra of eleven-dimensional supergravity backgrounds. As an application of this latter construction we show that supersymmetric supergravity backgrounds with enough supersymmetry are necessarily locally homogeneous.