@prefix vivo: .
@prefix edm: .
@prefix dcterms: .
@prefix dc: .
@prefix skos: .
@prefix ns0: .
vivo:departmentOrSchool "Non UBC"@en ;
edm:dataProvider "DSpace"@en ;
dcterms:creator "Michael Brannan"@en ;
dcterms:issued "2020-01-14T09:26:09Z"@en, "2019-07-17T09:04"@en ;
dcterms:description "A quantum permutation (or magic unitary) is given by a square matrix whose entries are self-adjoint projections acting on a common Hilbert space $H$ with the property that the row and column sums each add up to the identity operator. Quantum permutations are operator-valued analogues of ordinary permutation matrices and they arise naturally in both quantum group theory and also in the study of quantum strategies for certain non-local games. From the perspective of non-local games, it is often of great importance to know whether or not a quantum permutation (possibly satisfying some additional algebraic relations among its entries) admits a matrix model. I.e., can it be realized via operators on a finite-dimensional Hilbert space $H$ In this talk, I will explain how in the case of ``generic'' quantum permutations, matrix models abound. More precisely, the universal unital $\\ast$-algebra $A(N)$ generated by the coefficients of an $N\\times N$ quantum permutation is always residually finite dimensional (RFD). Our arguments are based on quantum group and subfactor techniques. As an application, we deduce that the II$_1$-factors associated to quantum permutation groups satisfy the Connes Embedding Conjecture. This is joint work with Alex Chirvasitu and Amaury Freslon."@en ;
edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/73318?expand=metadata"@en ;
dcterms:extent "60.0 minutes"@en ;
dc:format "video/mp4"@en ;
skos:note ""@en, "Author affiliation: Texas A&M University"@en ;
dcterms:spatial "Banff (Alta.)"@en ;
edm:isShownAt "10.14288/1.0388296"@en ;
dcterms:language "eng"@en ;
ns0:peerReviewStatus "Unreviewed"@en ;
edm:provider "Vancouver : University of British Columbia Library"@en ;
dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ;
dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ;
ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ;
ns0:scholarLevel "Researcher"@en ;
dcterms:isPartOf "BIRS Workshop Lecture Videos (Banff, Alta)"@en ;
dcterms:subject "Mathematics"@en, "Functional Analysis, Quantum Theory"@en ;
dcterms:title "Matrix models for quantum permutations"@en ;
dcterms:type "Moving Image"@en ;
ns0:identifierURI "http://hdl.handle.net/2429/73318"@en .