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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