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 AbstractA 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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