Self-Maps of Low Rank Lie Groups at Odd Primes

Grbić, Jelena ; Theriault, Stephen

Canadian journal of mathematics, Tome 62 (2010) no. 2, pp. 284-304

Résumé

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.

Détail

DOI : 10.4153/CJM-2010-017-0

Mots-clés : 55P45, 55Q05, 57T20, Lie group, self-map, H-map

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