Structure of Reductive Groups

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


By studying the actions of tori and their centralizers on G/B, we showed in Chapter IX that a reductive group is generated by the centralizers of singular tori (the latter being precisely the connected kernels of roots). Moreover, we showed that the quotient of such a centralizer by its center is essentially PGL(2, K). The goal of this chapter is a more detailed description of G: properties of the root system, structure of normal subgroups of G, “normal form” for elements of G, structure of parabolic subgroups.


Normal Subgroup Algebraic Group Weyl Group Parabolic Subgroup Reductive Group 
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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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