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Register a new userOperator algebras associated with unitary commutation relations
جبر المشغلات المرتبطة بعلاقات الترتيب الوحدي
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Authors
Stephen C. Power
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نحن نحدد الخوارزميات العاملة غير الذاتية المتأخرة مع المولدات $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ تحت علاقات التأطير الوحدة من النوع [ L_{e_i}L_{f_j} = sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}] حيث $u= (u_{i,j,k,l})$ هو مصفوفة وحدة بحجم $nm مرة nm$. هذه الخوارزميات التي تطور الخوارزميات التحليلية للرسوم البيانية من الرتبة 2 مع نقطة واحدة، تصنف حتى الإسومتري الإسومورفي باستخدام المصفوفة $u$.
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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