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Maximal abelian k-diagonalizable subgroups of reductive groups

  • Author / Creator
    Tan, Xiaobai
  • Given an algebraic group G over a field k and a k-algebra R, the role of maximal
    abelian k-diagonalizable subalgebras (MAD for short) of G(R) is the same as that
    the split maximal torus play in G(k). Let G be a reductive group such that the derived
    subgroup is simply connected and let Spec(R) be a connected reduced affine
    scheme. This dissertation is to studying conjugacy problems related to MADs in
    G(R). First, we provide the conjugacy theorem for regular MADs. For arbitrary
    MADs, the conjugacy theorem does not exist. But we give the structure of MADs
    in the classical groups of type A;B;C and D.

  • Subjects / Keywords
  • Graduation date
    Fall 2014
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R38C9RB04
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.