Operator algebras associated with unitary commutation relations

Power, Stephen and Solel, Baruch (2011) Operator algebras associated with unitary commutation relations. Journal of Functional Analysis, 260 (6). pp. 1583-1614. ISSN 0022-1236

Abstract

We define nonselfadjoint operator algebras with generators Le1,…,Len, Lf1,…,Lfm subject to the unitary commutation relations of the form (View the MathML source) 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.