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Self-Maps of Low Rank Lie Groups at Odd Primes
Jelena Grbić, Stephen Theriault
Journal:

Canadian Journal of Mathematics / Volume 62 / Issue 2 / 01 April 2010

Published online by Cambridge University Press:

20 November 2018, pp. 284-304

Print publication:

01 April 2010
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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.