Homology, Homotopy and Applications
Volume 20 (2018)
Samelson products in quasi-$p$-regular exceptional Lie groups
Pages: 185 – 208
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.
Samelson product, exceptional Lie group, quasi-$p$-regularity, $\mod p$ decomposition
2010 Mathematics Subject Classification
The second author was supported in part by JSPS KAKENHI (No. 25400087).
Received 4 May 2017
Received revised 21 September 2017
Published 24 January 2018