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

Journal article, 2018

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.