Exotic Group C*-algebras, Tensor Products, and Related Constructions
| dc.contributor.author | Wiersma, Matthew | |
| dc.date.accessioned | 2016-06-15T15:28:15Z | |
| dc.date.available | 2016-06-15T15:28:15Z | |
| dc.date.issued | 2016-06-15 | |
| dc.date.submitted | 2016-06-08 | |
| dc.description.abstract | Recently there has been a rejuvenated interest in exotic group C*-algebras, i.e., group C*-algebras which are "intermediate" to the full and reduced group C*-algebras. This resurgence began with the introduction of the class of group $L^p$-representations and their associated C*-algebras (a class of potentially exotic group C*-algebras) by Brown and Guentner. Unlike previous examples of exotic group C*-algebras, this class of examples is universally defined for all locally compact groups. In this thesis we compare this new class of exotic group C*-algebras to previously known examples of exotic group C*-algebras in several key examples and produces new examples of exotic group C*-algebras. Similar to the definition of exotic group C*-algebras, an exotic C*-tensor product is a C*-tensor product which is intermediate to the minimal and maximal C*-tensor products. Borrowing from the theory of $L^p$-representations, we construct many exotic C*-tensor products for group C*-algebras. We will also study the $L^p$-Fourier and Fourier-Stieltjes algebras of a locally compact group. These are ideals which of the Fourier-Stieltjes algebras containing the Fourier algebras and correspond to the class of $L^p$-representations. We study the structural properties of these algebras and classify the Fourier-Stieltjes spaces of SL(2,R) which are ideals in the Fourier-Stieltjes algebra. There are many different tensor products considered in the category of C*-algebras. In contrast, virtually the only tensor product ever considered for von Neumann algebras is the normal spatial tensor product. We propose a definition for what a generic tensor product in the category of von Neumann algebras should be and study properties of von Neumann algebras in relation to these tensor products. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/10548 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | Abstract harmonic analysis | en |
| dc.subject | C*-algebras | en |
| dc.subject | Tensor products | en |
| dc.subject | von Neumann algebras | en |
| dc.title | Exotic Group C*-algebras, Tensor Products, and Related Constructions | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Pure Mathematics | en |
| uws-etd.degree.discipline | Pure Mathematics | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws.contributor.advisor | Forrest, Brian | |
| uws.contributor.advisor | Spronk, Nicolaas | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |