| dc.contributor.advisor | Meyer, Ralf Prof. Dr. | |
| dc.contributor.author | Fabre Sehnem, Camila | |
| dc.date.accessioned | 2018-05-17T09:17:57Z | |
| dc.date.available | 2018-05-17T09:17:57Z | |
| dc.date.issued | 2018-05-17 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E3EC-A | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-6878 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | On C*-algebras associated to product systems | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Meyer, Ralf Prof. Dr. | |
| dc.date.examination | 2018-05-04 | |
| dc.description.abstracteng | We consider a class of Fell bundles over quasi-lattice ordered groups. We show that these are completely
determined by the positive fibres and that their cross sectional C*-algebras are relative Cuntz–Pimsner
algebras associated to simplifiable product systems of Hilbert bimodules. Conversely, we show that
such product systems can be naturally extended to Fell bundles and this correspondence is part of an
equivalence between bicategories. We also relate amenability for this class of Fell bundles to amenability
of quasi-lattice orders by showing that Fell bundles extended from free semigroups are amenable. A
similar result is proved for Baumslag–Solitar groups. Moreover, we construct a relative Cuntz–Pimsner
algebra of a compactly aligned product system as a quotient of the associated Nica–Toeplitz algebra.
We show that this construction yields a reflector from a bicategory of compactly aligned product
systems into its sub-bicategory of simplifiable product systems of Hilbert bimodules. We use this to
study Morita equivalence between relative Cuntz–Pimsner algebras.
In a second part, we let P be a unital subsemigroup of a group G. We propose an approach to
C*-algebras associated to product systems over P. We call the C*-algebra of a given product system E
its covariance algebra and denote it by A x_E P, where A is the coefficient C*-algebra. We prove that
our construction does not depend on the embedding P->G and that a representation of A x_E P is
faithful on the fixed-point algebra for the canonical coaction of G if and only if it is faithful on A.
We compare this with other constructions in the setting of irreversible dynamical systems, such as
Cuntz–Nica–Pimsner algebras, Fowler’s Cuntz–Pimsner algebra, semigroup C*-algebras of Xin Li and
Exel’s crossed products by interaction groups. | de |
| dc.contributor.coReferee | Buss, Alcides Prof. Dr. | |
| dc.subject.eng | Correspondence | de |
| dc.subject.eng | relative Cuntz--Pimsner algebra | de |
| dc.subject.eng | correspondence bicategories | de |
| dc.subject.eng | product system | de |
| dc.subject.eng | Fell bundle over quasi-lattice ordered group | de |
| dc.subject.eng | covariance algebra | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E3EC-A-6 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematik (PPN61756535X) | de |
| dc.identifier.ppn | 1022445758 | |