Title page for ETD etd-07262006-091536


Type of Document Dissertation
Author Fulton, Melanie B.
URN etd-07262006-091536
Title The Quantum Automorphism Group and Undirected Trees
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Letzter, Gail Committee Chair
Farkas, Daniel R. Committee Member
Haskell, Peter E. Committee Member
Linnell, Peter A. Committee Member
Keywords
  • Automorphism Group
  • Hopf Algebras
  • Quantum Automorphism
Date of Defense 2006-07-21
Availability unrestricted
Abstract
A classification of all undirected trees with automorphism group

isomorphic to $(Z_2)^l$ is given in terms of a vertex partition

called a refined star partition. Recently the notion of a quantum

automorphism group has been defined by T. Banica and J. Bichon.

The quantum automorphism group is similar to the classical

automorphism group, but has relaxed commutivity. The

classification of all undirected trees with automorphism group

isomorphic to $(Z_2)^l$ along with a similar classification of all

undirected asymmetric trees is used to give some insight into the

structure of the quantum automorphism group for such graphs.

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