Double Crossproducts of Hopf* Algebras, Discrete Quantum Groups and Amenable Groups
Fitzgerald, Kevin Francis
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https://hdl.handle.net/2142/86940
Description
Title
Double Crossproducts of Hopf* Algebras, Discrete Quantum Groups and Amenable Groups
Author(s)
Fitzgerald, Kevin Francis
Issue Date
1997
Doctoral Committee Chair(s)
Ruan, Zhong-Jin
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, General
Language
eng
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.
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