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 Title: Double Crossproducts of Hopf* Algebras, Discrete Quantum Groups and Amenable Groups Author(s): Fitzgerald, Kevin Francis Doctoral Committee Chair(s): Ruan, Zhong-Jin Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Physics, General Abstract: In Appendix A, we consider a third construction, the bicrossproduct which is a simultaneous cross product/cross coproduct construction. We find conditions which ensure that the bicrossproduct of two Hopf $\sp{\*}$ algebras is a Hopf $\sp{\*}$ algebra. In Appendix B, we provide physical motivation for studying bicrossproducts by describing a possible theory of quantum gravity where the algebra of quantum observables is a bicrossproduct. Issue Date: 1997 Type: Text Language: English Description: 132 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997. URI: http://hdl.handle.net/2142/86940 Other Identifier(s): (MiAaPQ)AAI9717274 Date Available in IDEALS: 2015-09-28 Date Deposited: 1997
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