Homology, Homotopy and Applications

Volume 20 (2018)

Number 1

Samelson products in quasi-$p$-regular exceptional Lie groups

Pages: 185 – 208

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n1.a11

Authors

Sho Hasui (Faculty of Liberal Arts and Sciences, Osaka Prefecture University, Sakai, Japan)

Daisuke Kishimoto (Department of Mathematics, Kyoto University, Kyoto, Japan)

Toshiyuki Miyauchi (Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka, Japan)

Akihiro Ohsita (Faculty of Economics, Osaka University of Economics, Osaka, Japan)

Abstract

There is a product decomposition of a compact connected Lie group $G$ at the prime $p$, called the $\mod p$ decomposition, when $G$ has no $p$-torsion in homology. Then in studying the multiplicative structure of the $p$-localization of $G$, the Samelson products of the factor space inclusions of the $\mod p$ decomposition are fundamental. This paper determines the (non-)triviality of these fundamental Samelson products in the $p$-localized exceptional Lie groups when the factor spaces are of rank $\leqslant 2$, that is, $G$ is quasi-$p$-regular.

Keywords

Samelson product, exceptional Lie group, quasi-$p$-regularity, $\mod p$ decomposition

2010 Mathematics Subject Classification

55P35, 57T10

Received 4 May 2017

Received revised 21 September 2017

Published 24 January 2018