Locally compact quantum groups.
Date of Award
Mathematics and Statistics
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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.
He, Andong., "Locally compact quantum groups." (2006). Electronic Theses and Dissertations. 2635.