Notes on generalised spin structures
Differential Geometry
2025-11-06 v1 High Energy Physics - Theory
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.
Cite
@article{arxiv.2511.03627,
title = {Notes on generalised spin structures},
author = {Andrew D. K. Beckett},
journal= {arXiv preprint arXiv:2511.03627},
year = {2025}
}