Title page for ETD etd-04182003-143702


Type of Document Dissertation
Author Siehler, Jacob A.
Author's Email Address jsiehler@math.vt.edu
URN etd-04182003-143702
Title Near-Group Categories
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Quinn, Frank S. Committee Chair
Green, Edward L. Committee Member
Haskell, Peter E. Committee Member
Linnell, Peter A. Committee Member
Shimozono, Mark M. Committee Member
Keywords
  • monoidal categories
  • braided categories
  • quantum field theory
Date of Defense 2003-04-18
Availability unrestricted
Abstract
We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object, so-called near-group categories. Data describing the fusion rule is reduced to an abelian group G and a nonnegative integer k. Conditions are given, in terms of G and k, for the existence or nonexistence of coherent associative structures for such fusion rules (ie, solutions to MacLane's pentagon equation). An explicit construction of matrix solutions to the pentagon equations is given for the cases where we establish existence, and classification of the distinct solutions is carried out partially. Many of these associative structures also support (braided) commutative and tortile structures and we indicate when the additional structures are possible. Small examples are presented in detail suitable for use in computational applications.
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