Vol. 63, No. 1, 1976

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Fixed points of automorphisms of compact Lie groups

Robert F. Brown

Vol. 63 (1976), No. 1, 79–87

Hopf’s proof that the real Čech cohomology H(G) of a compact, connected Lie group G is an exterior algebra with odd-dimensional generators was followed by a demonstration that the number of such generators is equal to the rank of the group, that is, to the dimension of a maximal torus. We show that the latter result is a special case of a relationship between an automorphism of such a group and the automorphism it induces on the cohomology.

Mathematical Subject Classification
Primary: 57E15, 57E15
Received: 30 April 1975
Published: 1 March 1976
Robert F. Brown
Department of Mathematics
University of California, Los Angeles
Los Angeles CA 90095-1555
United States