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Semisimple and Unipotent Elements

  • James E. Humphreys
Part of the Graduate Texts in Mathematics book series (GTM, volume 21)

Abstract

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).

Keywords

Algebraic Group Closed Subgroup Finite Order Free Abelian Group Semisimple Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • James E. Humphreys
    • 1
  1. 1.University of MassachusettsAmherstUSA

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