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SAMELSON PRODUCTS IN p-REGULAR SO(2n) AND ITS HOMOTOPY NORMALITY

Published online by Cambridge University Press:  07 February 2017

DAISUKE KISHIMOTO  and
MITSUNOBU TSUTAYA
DAISUKE KISHIMOTO
Affiliation:
Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan e-mail: kishi@math.kyoto-u.ac.jp
MITSUNOBU TSUTAYA
Affiliation:
Faculty of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan e-mail: tsutaya@math.kyushu-u.ac.jp
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Abstract

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A Lie group is called p-regular if it has the p-local homotopy type of a product of spheres. (Non)triviality of the Samelson products of the inclusions of the factor spheres into p-regular SO(2n(p) is determined, which completes the list of (non)triviality of such Samelson products in p-regular simple Lie groups. As an application, we determine the homotopy normality of the inclusion SO(2n − 1) → SO(2n) in the sense of James at any prime p.

Keywords

55Q15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 165 - 174
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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