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Representations of affine truncations of representation involutive-semirings of Lie algebras and root systems of higher type

  • Author / Creator
    Graves, Timothy W
  • An important component of a rational conformal field theory is a representation of a certain involutive-semiring. In the case of Wess-Zumino-Witten models, the involutive-semiring is an affine truncation of the representation involutive-semiring of a finite-dimensional semisimple Lie algebra. We show how root systems naturally correspond to representations of an affine truncation of the representation involutive-semiring of sl_2(C). By reversing this procedure, one can, to a representation of an affine truncation of the representation involutive-semiring of an arbitrary finite-dimensional semisimple Lie algebra, associate a root system and a Cartan matrix of higher type. We show how this same procedure applies to a special subclass of representations of the nontruncated representation involutive-semiring, leading to higher-type analogues of the affine Cartan matrices. Finally, we extend the known results for sl_3(C) with a symmetric classification, a construction, and a list of computer-generated examples.

  • Subjects / Keywords
  • Graduation date
    2011-06
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3D946
  • 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
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Supervisor / co-supervisor and their department(s)
    • Gannon, Terry (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Cliff, Gerald (Mathematical and Statistical Sciences)
    • Czarnecki, Andrei (Physics)