Dilations and Higher Rank Operator Algebras - with Applications
Lead Research Organisation:
Lancaster University
Department Name: Mathematics and Statistics
Abstract
This project has several strands with a common theme of `dilation', whereby a mathematical object is viewed as a part of a larger, but simpler, construction. By bringing together experts, all of whom have proven records in collaboration as well as research, our plan is to make progress in the following areas.* Analytic Toeplitz algebras: classification of subalgebras, development of representation and dilation theory.* Noncommutative dynamics: computation of invariants and classification of cocycles.* Quantum computation and information: mathematical problems such as the estimation of states.Keen interaction of the proposed visitors with research students, postdocs, other visitors and colleagues of the investigators, for example through seminars, is also anticipated.
Organisations
People |
ORCID iD |
Stephen Power (Principal Investigator) | |
J. Lindsay (Co-Investigator) |
Publications
Davidson K
(2008)
Atomic representations of rank 2 graph algebras
in Journal of Functional Analysis
Olphert S
(2008)
Higher Rank Wavelets
Olphert S
(2018)
Higher Rank Wavelets
in Canadian Journal of Mathematics
Power S
(2011)
Operator algebras associated with unitary commutation relations
in Journal of Functional Analysis
Description | (i) We classified various classes of non-self-adjoint operator algebras. (ii) We developed a theory of Higher Rank Wavelets, (iii) We developed some methods in quantum cryptography and error correction |
Exploitation Route | (see the 2008 report in the URL) |
Sectors | Other |
URL | http://www.maths.lancs.ac.uk/~power/vfREPORTaug08.pdf |