Operator algebras associated with unitary commutation relations

We define nonselfadjoint operator algebras with generators Le1, . . . , Len,Lf1, . . . , Lfm subject to the unitary commutation relations of the form LeiLfj = k,l ui,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. © 2010 Elsevier Inc. All rights reserved.