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Rational homotopy equivalences of Lie type

Published online by Cambridge University Press:  24 October 2008

Stefan Papadima
Stefan Papadima
Affiliation:
Department of Mathematics, Increst, B-dul Pacii 220, 79622 Bucharest, Romania
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Consider K⊂G, a proper pair of equal rank compact connected Lie groups. It is known (see [6], proof of theorem 1·1) that the group of self-homotopy equivalences of the rationalization of G/K is (anti)isomorphic, in a natural way, to the group of graded algebra automorphisms of H*(G/K; ℚ). On one side of the matter there is the fact that AutH*(G/K; ℚ) almost gives the integral picture of the group of homotopy classes of the self-homotopy equivalences of G/K, that is, up to a finite ambiguity and up to grading automorphisms of H*(G/K; ℚ) (i.e. those acting on H2i as λi.id, for some non-zero λ∈ℚ): see also [6]. On the other side there is the classical description by Borel[2] of H*(G/K; ℚ) in terms of invariants of Weyl groups, which gives hope for a satisfactory understanding of AutH*(G/K; ℚ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 1 , July 1988 , pp. 65 - 80
Copyright
Copyright © Cambridge Philosophical Society 1988

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