Semisimple and Unipotent Elements

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


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).


Algebraic Group Closed Subgroup Finite Order Free Abelian Group Semisimple Element 


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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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