The isomorphism type of the centralizer of an element in a Lie group
Abstract
Let G be an 1-connected simple Lie group, and let x∈G be a group element. We determine the isomorphism type of the centralizer Cx in term of a minimal geodesic joinning the group unit e∈G to x. This result is applied to classify the isomorphism types of maximal subgroups of maximal rank of G, and the isomorphism types of parabolic subgroups of G.
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