A semisimple Lie group is a type of Lie group that has no nontrivial connected normal subgroups that are abelian, meaning it cannot be broken down into simpler groups while still preserving its structure. These groups are important in the study of symmetry and represent fundamental building blocks for more complex structures. In the context of representation theory and the study of weights, semisimple Lie groups reveal intricate relationships through their representations and the associated Weyl group.
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