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

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 (non-)triviality of these fundamental Samelson products in the $p$-localized exceptional Lie groups when the factor spaces are of rank $\le 2$, that is, $G$ is quasi-$p$-regular.

22 pages, 0 figure

References in corpus (1)

• Samelson products in p-regular SO(2n) and its homotopy normality

Cited by in corpus (1)

• Higher homotopy commutativity in localized Lie groups and gauge groups