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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
    2014-11
  • 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.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Jochen Kuttle (Mathematical and Statistical Sciences)
    • Arturo Pianzola (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Vladimir Chernousov (Mathematical and Statistical Sciences)
    • Vincent Bouchard (Mathematical and Statistical Sciences)