Date of Award
2006
Publication Type
Master Thesis
Degree Name
M.Sc.
Department
Mathematics and Statistics
Keywords
Mathematics.
Rights
info:eu-repo/semantics/openAccess
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Abstract
In this thesis, we approach quantum groups in two ways. One is through multiplier Hopf *-algebra with integrals, which is a *-algebra with a comultiplication and invariant integrals on it. The second one is an operator algebra way, the main component of this thesis, which introduces the category of locally compact quantum groups. In both frameworks we obtain a generalization of the Pontryagin duality theorem for locally compact abelian groups. Locally compact quantum groups and their dual quantum groups both in C*-algebra and von Neumann algebra settings are studied. We then focus on the classical locally compact quantum group with C0(G) in the C*-algebra setting and Linfinity(G) in the von Neumann algebra setting. We use them to interpret the motivation of defining a general locally compact quantum group.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2006 .H4. Source: Masters Abstracts International, Volume: 45-01, page: 0333. Thesis (M.Sc.)--University of Windsor (Canada), 2006.
Recommended Citation
He, Andong, "Locally compact quantum groups." (2006). Electronic Theses and Dissertations. 2635.
https://scholar.uwindsor.ca/etd/2635