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AUTOMORPHISMS AND TWISTED FORMS OF DIFFERENTIAL LIE CONFORMAL SUPERALGEBRAS

  • Author / Creator
    Chang, Zhihua
  • Given a conformal superalgebra A over an algebraically closed field k of characteristic zero, a twisted loop conformal superalgebra L based on A has a differential conformal superalgebra structure over the differential Laurent polynomial ring D. In this context, L is a D_m/D–form of A \otimes D with respect to an étale extension of differential rings D_m/D, and hence is a \hat{D}/D–form of A. Such a perspective reduces the problem of classifying the twisted loop conformal superalgebras based on A to the computation of the non-abelian cohomology set of its automorphism group functor. The primary goal of this dissertation is to classify the twisted loop conformal superalgebras based on A when A is one of the N=1,2,3 and (small or large) N=4 conformal superalgebras. To achieve this, we first explicitly determined the automorphism group of the \hat{D}–conformal superalgebra A\otimes\hat{D} in each case. We then computed the corresponding non-abelian continuous cohomology set, and obtained the classification of our objects up to isomorphism over D. Finally, by applying the so-called “centroid trick”, we deduced from isomorphisms over D to isomorphisms over k, thus accomplishing the classification over k. Additionally, in order to understand the representability of the automorphism group functors of the N=1,2,3 and small N = 4 conformal superalgebras, we discuss the (R,d)–points of these automorphism group functors for an arbitrary differential ring (R,d). In particular, if R is an integral domain with certain additional assumptions in the small N = 4 case), these automorphism groups have been completely determined.

  • Subjects / Keywords
  • Graduation date
    2013-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3FT8DW2S
  • 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)
    • Pianzola, Arturo (Department of Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Bouchard, Vincent (Department of Mathematical and Statistical Sciences)
    • Chernousov, Vladimir (Department of Mathematical and Statistical Sciences)
    • Yui, Noriko (Queen's University, Department of Mathematics and Statistics)
    • Kuttler, Jochen (Department of Mathematical and Statistical Sciences)