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FAITHFULNESS OF THE FOCK REPRESENTATION OF THE C*-ALGEBRA GENERATED BY q(ij)-COMMUTING ISOMETRIES

Journal article
Authors Oleksii Kuzmin
N. Pochekai
Published in Journal of Operator Theory
Volume 80
Issue 1
Pages 77-93
ISSN 0379-4024
Publication year 2018
Published at Department of Mathematical Sciences
Pages 77-93
Language en
Links dx.doi.org/10.7900/jot.2017jun01.21...
Keywords C*-algebra, Cuntz algebra, nuclear, q-deformation, Fock representation, operator algebras, q-commutation relations, statistics, Mathematics
Subject categories Statistics, Mathematics

Abstract

We consider the C*-algebra Isom(Q), where Q = (q(ij))(i,j=1)(n) is a matrix of complex numbers. This algebra is generated by n isometrics a(1), . . . , a(n) satisfying the relations a(i)*a(j) = q(ij)a(j)a(i)*, i not equal j with max vertical bar q(ij)vertical bar < 1. This C*-algebra is shown to be nuclear. We prove that the Fock representation of Isom(Q) is faithful. Further we describe an ideal in Isom(Q) which is isomorphic to the algebra of compact operators.

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