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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The Lefschetz number of self-maps of Lie groups


Author: Hai Bao Duan
Journal: Proc. Amer. Math. Soc. 104 (1988), 1284-1286
MSC: Primary 55M20; Secondary 57T10
DOI: https://doi.org/10.1090/S0002-9939-1988-0935107-8
MathSciNet review: 935107
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Abstract: In this note we present a simple approach to the Lefschetz number for the self-maps of Lie groups. As an application it is proved that for any map $ f:G \to G$ of a compact connected Lie group $ G$, there is a solution to $ {(f(x))^k} = x$ for some $ k \leq \leftthreetimes + 1$, where $ \leftthreetimes $ is the rank of the group $ G$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0935107-8
Keywords: Lefschetz number, mapping degree, fixed point, Lie group, adjoint representation, exterior algebra, primitive elements in the cohomology of a Lie group, Vandermonde matrix
Article copyright: © Copyright 1988 American Mathematical Society

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