The isomorphism type of the centralizer of an element in a Lie group

Details The isomorphism type of the centralizer of an element in a Lie group The isomorphism type of the centralizer of an element in a Lie group

2012-01-16

arxiv.org/abs/1201.3394v2

Mathematics

Group Theory

35 pages; 5 tables

Scientific paper

Let G be an 1-connected simple Lie group, and let x\inG be a group element.
We determine the isomorphism type of the centralizer C_{x} in term of a minimal
geodesic joinning the group unit e\inG 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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