Canad. J. Math. 62(2010), 284-304
Printed: Apr 2010
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 $[G,G]$ when the rank of G is low and in certain cases describe the set of homotopy classes of multiplicative self-maps $H[G,G]$. The low rank condition gives G certain structural properties which make calculations accessible. Several examples and applications are given.
Lie group, self-map, H-map
55P45 - $H$-spaces and duals
55Q05 - Homotopy groups, general; sets of homotopy classes
57T20 - Homotopy groups of topological groups and homogeneous spaces