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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Group actions on spin manifolds


Author: G. Chichilnisky
Journal: Trans. Amer. Math. Soc. 172 (1972), 307-315
MSC: Primary 53C50; Secondary 57D15, 83.53
DOI: https://doi.org/10.1090/S0002-9947-1972-0309033-4
MathSciNet review: 0309033
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Abstract: A generalization of the theorem of V. Bargmann concerning unitary and ray representations is obtained and is applied to the general problem of lifting group actions associated to the extension of structure of a bundle. In particular this is applied to the Poincaré group $ \mathcal{P}$ of a Lorentz manifold $ M$. It is shown that the topological restrictions needed to lift an action in $ \mathcal{P}$ are more stringent than for actions in the proper Poincaré group $ \mathcal{P}_ \uparrow ^ + $. Similar results hold for the Euclidean group of a Riemannian manifold.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0309033-4
Keywords: Bargmann theorem, extension of structure, spinors, lifted action, projective representation, Poincaré group, Euclidean group
Article copyright: © Copyright 1972 American Mathematical Society