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NOTE ON SAMELSON PRODUCTS IN EXCEPTIONAL LIE GROUPS

Part of: Homology and homotopy of topological groups and related structures Homotopy groups

Published online by Cambridge University Press:  24 November 2020

DAISUKE KISHIMOTO ,
AKIHIRO OHSITA  and
MASAHIRO TAKEDA
DAISUKE KISHIMOTO
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan e-mail: kishi@math.kyoto-u.ac.jp
AKIHIRO OHSITA
Affiliation:
Faculty of Economics, Osaka University of Economics, Osaka 533-8533, Japan e-mail: ohsita@osaka-ue.ac.jp
MASAHIRO TAKEDA
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan e-mail: m.takeda@math.kyoto-u.ac.jp
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Abstract

We determine the (non-)triviality of Samelson products of inclusions of factors of the mod p decomposition of $G_{(p)}$ for $(G,p)=(E_7,5),(E_7,7),(E_8,7)$. This completes the determination of the (non-)triviality of those Samelson products in p-localized exceptional Lie groups when G has p-torsion-free homology.

MSC classification

Primary: 55Q15: Whitehead products and generalizations
Secondary: 57T10: Homology and cohomology of Lie groups

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 3 , September 2021 , pp. 741 - 752
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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