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

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

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 〈1G,1G〉 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 〈1G,1G〉 for all p-regular Lie groups and give bounds of the orders of 〈1G,1G〉 for certain quasi-p-regular Lie groups.

Homotopy nilpotence, Lie group, Samelson products
0166-8641
210-227
So, Tseleung
175505d4-3a13-4bb3-8f99-f24502cfcc2d
So, Tseleung
175505d4-3a13-4bb3-8f99-f24502cfcc2d

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).

Record type: Article

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 〈1G,1G〉 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 〈1G,1G〉 for all p-regular Lie groups and give bounds of the orders of 〈1G,1G〉 for certain quasi-p-regular Lie groups.

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More information

Accepted/In Press date: 14 March 2018
e-pub ahead of print date: 16 March 2018
Published date: 15 May 2018
Keywords: Homotopy nilpotence, Lie group, Samelson products

Identifiers

Local EPrints ID: 421600
URI: https://eprints.soton.ac.uk/id/eprint/421600
ISSN: 0166-8641
PURE UUID: 70f0dd3a-6f69-48f7-81d3-0ff563131f8b

Catalogue record

Date deposited: 15 Jun 2018 16:31
Last modified: 13 Mar 2019 18:41

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Author: Tseleung So

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