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

So, Tseleung (2018) The odd primary order of the commutator on low rank Lie groups. Topology and its Applications, 240, 210-227. (doi:10.1016/j.topol.2018.03.012).

Abstract

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 〈ı,ı〉 of the inclusion ı: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.

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