The odd primary order of the commutator on low rank Lie groups

摘要

Let G be a simple, simply-connected, compact Lie group of low rank relative to a fixed prime p. After localization at p, there is a space A which "generates" G in a certain sense. Assuming G satisfies a homotopy nilpotency condition relative to p, we show that the Samelson product (1(G), 1(G)) of the identity of G equals the order of the Samelson product (l, l) of the inclusion l : A - G. Applying this result, we calculate the orders of (1(G), 1(G)) for all p-regular Lie groups and give bounds of the orders of (1(G), 1(G)) for certain quasi-p-regular Lie groups. (C) 2018 Elsevier B.V. All rights reserved.