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Self-Maps of Low Rank Lie Groups at Odd Primes

Published online by Cambridge University Press:  20 November 2018

Jelena Grbić  and
Stephen Theriault
Jelena Grbić
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK, e-mail: [email protected]
Stephen Theriault
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, UK, e-mail: [email protected]
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Abstract

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Let $G$ be a simple, compact, simply-connected Lie group localized at an odd prime $p$. We study the group of homotopy classes of self-maps $\left[ G,\,G \right]$ when the rank of $G$ is low and in certain cases describe the set of homotopy classes of multiplicative self-maps $H\left[ G,\,G \right]$. The low rank condition gives $G$ certain structural properties which make calculations accessible. Several examples and applications are given.

Keywords

55P4555Q0557T20Lie groupself-mapH-map
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 2 , 01 April 2010 , pp. 284 - 304
Copyright
Copyright © Canadian Mathematical Society 2010

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