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arXiv · 2511.03627

Notes on generalised spin structures

Andrew D. K. Beckett
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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.

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Andrew D. K. Beckett. 2025-11-05. Notes on generalised spin structures. https://arxiv.org/abs/2511.03627

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