Notes on generalised spin structures

2025/11/05 by Andrew D. K. Beckett, Beckett, Andrew D. K. · 1 voice
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Covariant derivative #Covariant transformation #Extension (predicate logic) #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie derivative #Nonlinear Waves and Solitons #Representation (politics) #Spin (aerodynamics) #Symmetry (geometry) #hep-th #math.DG

paper · pdf · open access · doi:10.48550/arxiv.2511.03627

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/11/05 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/28

Abstract

We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop a covariant Cartan calculus. We introduce an extension of the Lie algebra of Killing vectors, the symmetry algebra, and show that it has a representation on sections of associated bundles. We discuss homogeneous generalised spin structures and provide a characterisation of them in terms of lifts of the isotropy representation.

Citations

• On the heat equation and the index theorem

Discussions

• Read later arxiv.org/abs/2511.03627 [bsky, 0 points, 0 comments]

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