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Transformation groups resembling the adjoint representation


Author: R. W. Sullivan
Journal: Proc. Amer. Math. Soc. 47 (1975), 491-494
MSC: Primary 57E15
DOI: https://doi.org/10.1090/S0002-9939-1975-0368054-4
MathSciNet review: 0368054
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Abstract: If $ G$ is a compact, connected Lie group, the isotropy subgroups of the adjoint representation of $ G$ are connected and the dimension of the fixed point set of a maximal torus of $ G$ is equal to the the rank of $ G$. Results similar to these are given when $ G$ acts differentiably on an integral cohomology sphere and has the adjoint representation as weak linear model. This is done by analyzing an induced action of the Weyl group of $ G$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0368054-4
Keywords: Weyl group, adjoint representation, cohomology sphere
Article copyright: © Copyright 1975 American Mathematical Society