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

Abstract

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 $\mathrm{SO}(2n{)}_{(p)}$ 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 $\mathrm{SO}(2n-1)\to \mathrm{SO}(2n)$ in the sense of James at any prime $p$.

9 pages, some results on homotopy normality are added

Cited by in corpus (4)

• Samelson products in quasi-$p$-regular exceptional Lie groups
• Note on Samelson products in exceptional Lie groups
• Higher homotopy associativity in the Harris decomposition of Lie groups
• Higher homotopy normalities in topological groups