Operator algebras associated with unitary commutation relations

Abstract

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 $u$.

38 pages

References in corpus (2)

• Higher rank graph C*-algebras
• Regular dilations of representations of product systems

Cited by in corpus (4)

• CP-Semigroups and Dilations, Subproduct Systems and Superproduct Systems: The Multi-Parameter Case and Beyond
• Poisson transform for higher-rank graph algebras and its applications
• On isometric dilations of product systems of C*-correspondences and applications to families of contractions associated to higher-rank graphs
• Biholomorphisms of the unit ball of C^n and semicrossed products