Semisimple and Unipotent Elements
The Jordan normal form (diagonal plus nilpotent) for a single linear transformation has a multiplicative counterpart (diagonal times unipotent) in GL(n, K). The main result of this section (Theorem 15.3) asserts that a closed subgroup of GL(n, K) contains these components of each of its elements. From this we can deduce to some extent the structure of a commutative algebraic group (15.5).
KeywordsAlgebraic Group Closed Subgroup Finite Order Free Abelian Group Semisimple Element
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