Abstract :
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.
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