A commutativity criterion for closed subgroups of compact Lie groups.
Author: Joseph A. Wolf
Journal: Proc. Amer. Math. Soc. 27 (1971), 619-622
MSC: Primary 22.50; Secondary 17.00
MathSciNet review: 0277663
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Abstract: Let be a closed subgroup of a compact Lie group . If the identity component is commutative, and if the order of is prime to the order of the Weyl group of , then it is shown that is commutative. If is a classical group this extends a theorem of Burnside on finite linear groups. If is exceptional this gives some information on Cayley-Dickson algebras, Jordan algebras and the Cayley protective plane.
Keywords: Lie group, closed subgroup, commutative subgroup, Weyl group, linear group, Jordan algebra
Article copyright: © Copyright 1971 American Mathematical Society