Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T06:36:56.039Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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
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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, J. F., Lectures on Exceptional Lie Groups, Chicago Lectures in Mathematics (University of Chicago Press, Chicago, IL, 1996).Google Scholar
Hamanaka, H. and Kono, A., A note on Samelson products and mod p cohomology of classifying spaces of the exceptional Lie groups, Topology Appl. 157(2) (2010), 393–400.CrossRefGoogle Scholar
Hasui, S., Kishimoto, D., Miyauchi, T. and Ohsita, A., Samelson products in quasi-p-regular exceptional Lie groups, Homology Homotopy Appl. 20(1) (2018), 185–208.CrossRefGoogle Scholar
Hasui, S., Kishimoto, D. and Ohsita, A., Samelson products in p-regular exceptional Lie groups, Topology Appl. 178 (2014), 17–29.CrossRefGoogle Scholar
Hasui, S., Kishimoto, D., So, T. and Theriault, S., Odd primary homotopy types of the gauge groups of exceptional Lie groups, Proc. Amer. Math. Soc. 147(4) (2019), 1751–1762.CrossRefGoogle Scholar
Kaji, S. and Kishimoto, D., Homotopy nilpotency in p-regular loop spaces, Math. Z. 264(1) (2010), 209–224.CrossRefGoogle Scholar
Kishimoto, D. and Tsutaya, M., Samelson products in p-regular SO(2n) and its homotopy normality, Glasg. Math. J. 60(1) (2018), 165–174.CrossRefGoogle Scholar
Kono, A. and Ōshima, H., Commutativity of the group of self homotopy classes of Lie groups, Bull. London Math. Soc. 36(1) (2004), 37–52.CrossRefGoogle Scholar
Mimura, M., Nishida, G. and Toda, H., Mod p decomposition of compact Lie groups, Publ. Res. Inst. Math. Sci. 13(3) (1977/78), 627–680.CrossRefGoogle Scholar
Shay, P. B., mod p Wu formulas for the Steenrod algebra and the Dyer-Lashof algebra, Proc. Amer. Math. Soc. 63(2) (1977), 339–347.CrossRefGoogle Scholar
Theriault, S. D., Odd primary homotopy decompositions of gauge groups, Alg. Geom. Topol. 10(1) (2010), 535–564.CrossRefGoogle Scholar