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Geometric and Graphical Study of 1-Dimensional N-Extended Supersymmetry Algebras

  • Author / Creator
    Chinen, Minako
  • In this thesis, we explore the relationship between graphical representations of the 1-dimensional N-extended supersymmetry algebra called Adinkras, compact Riemann surfaces, and quivers. An Adinkra is a graph which was originated in physics to study off-shell representations of the supersymmetry algebra. We focus on N = 4 Adinkras in this thesis. From a mathematical point of view, Adinkras are dessins d'enfants. Using this fact, we explain Adinkras as branched covering spaces for partricular dessins. We also demonstrate how to generate a quiver QA from an Adinkra A and relate QA to the noncommutative generalization of Calabi-Yau varieties called Calabi-Yau algebras. More precisely, we construct a Jacobi algebra of Q_A with a superpotential. However, in general, a Jacobi algebra generated in this way need not be a Calabi-Yau algebra. We show that Jacobi algebras of quivers constructed from Adinkras are Calabi-Yau algebras of dimension 3. We also discuss Jacobians of the Riemann surfaces in which Adinkras are embedded using isogenous decompositions of Jacobians of the Adinkra Riemann surfaces.

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3TX35N9P
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.