"Non UBC"@en .
"DSpace"@en .
"Michael Brannan"@en .
"2020-01-14T09:26:09Z"@en .
"2019-07-17T09:04"@en .
"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 .
"https://circle.library.ubc.ca/rest/handle/2429/73318?expand=metadata"@en .
"60.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Texas A&M University"@en .
"Banff (Alta.)"@en .
"10.14288/1.0388296"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Researcher"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Functional Analysis, Quantum Theory"@en .
"Matrix models for quantum permutations"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/73318"@en .