Vol. 69, No. 2, 1977

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Cohomology of homomorphisms of Lie algebras and Lie groups

Robert F. Brown

Vol. 69 (1977), No. 2, 325–332

Given compact, connected Lie groups G1 and G2 and given h : G1 G2 a homomorphism with kernel K, let Ph : PH(G2) PH(G1) be the homomorphism of the primitives in the real cohomology induced by h. We prove that if the rank of G2 is greater than or equal to the rank of G1, then the dimension of the kernel of Ph is greater than or equal to the rank of K. We discuss when the inequality is an equality and we use the inequality to study when the hypothesis that Ph is an isomorphism implies that h itself is an isomorphism.

Mathematical Subject Classification
Primary: 57F10, 57F10
Received: 25 October 1976
Published: 1 April 1977
Robert F. Brown
Department of Mathematics
University of California, Los Angeles
Los Angeles CA 90095-1555
United States