2025/11/10 by Andrew D. K. Beckett, Beckett, Andrew D. K.
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Affine connection #Algebraic number #Connection (principal bundle) #Dirac (video compression format) #Homotopy and Cohomology in Algebraic Topology #Infinitesimal #Manifold (fluid mechanics) #Spin connection #Spinor #Subalgebra #Superalgebra
paper · pdf · open access · doi:10.48550/arxiv.2511.07246
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28
We define the notion of a Killing (super)algebra for a connection on a spinor bundle associated to a generalised spin structure on a pseudo-Riemannian manifold of any signature. We are led naturally to include in the even subspace not only Killing vectors but also certain infinitesimal gauge transformations, and we show that the definition of the (super)algebra requires, in addition to the spinor connection and a Dirac current, a map to pair spinor fields into infinitesimal gauge transformations. We show that these (super)algebras are filtered subdeformations of (an analogue of) the Poincaré superalgebra extended by the R-symmetry algebra. By employing Spencer cohomology, we study such deformations from a purely algebraic point of view and, at least in the case of Lorentzian signature and high supersymmetry, identify the subclass of deformations to which the Killing superalgebras belong. Finally, we show that, with some caveats, one can reconstruct a supersymmetric background geometry from such a deformation as a homogeneous space on which the deformation is realised as a subalgebra of the Killing superalgebra.