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Higher homotopy associativity in the Harris decomposition of Lie groups

Part of: Homotopy groups Homotopy theory

Published online by Cambridge University Press:  11 September 2019

Daisuke Kishimoto  and
Toshiyuki Miyauchi
Daisuke Kishimoto
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan (kishi@math.kyoto-u.ac.jp)
Toshiyuki Miyauchi
Affiliation:
Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan (miyauchi@math.sci.fukuoka-u.ac.jp)
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Abstract

For certain pairs of Lie groups (G, H) and primes p, Harris showed a relation of the p-localized homotopy groups of G and H. This is reinterpreted as a p-local homotopy equivalence G ≃ (p)H × G/H, and so there is a projection G(p) → H(p). We show how much this projection preserves the higher homotopy associativity.

Keywords

Lie groupmod p decompositionhigher homotopy associativityhigher homotopy commutativity

MSC classification

Primary: 55P60: Localization and completion
Secondary: 55P35: Loop spaces 55Q15: Whitehead products and generalizations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 2982 - 3000
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Copyright
Copyright © 2019 The Royal Society of Edinburgh

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