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We define nonselfadjoint operator algebras with generators Le1,…,Len,Lf1,…,Lfm subject to the unitary commutation relations of the formLeiLfj=∑k,lui,j,k,lLflLek where u=(ui,j,k,l) is an nm×nm unitary matrix. These algebras, which generalise the analytic Toeplitz algebras of rank 2 graphs with a single vertex, are classified up to isometric isomorphism in terms of the matrix u.
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