Operator algebras associated with unitary commutation relations

Details Operator algebras associated with unitary commutation relations Operator algebras associated with unitary commutation relations

2007-04-02

arxiv.org/abs/0704.0079v1

Mathematics

Operator Algebras

38 pages

Scientific paper

We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u= (u_{i,j,k,l})$ is an $nm \times nm$ 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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