Quantization and dynamisation of Trace-Poisson brackets
  The quantization problem for the trace-bracket algebra, derived from double Poisson brackets, is discussed. We obtain a generalization of the boundary YBE (or so-called ABCD-algebra) for the quantization of quadratic trace-brackets. A dynamical deformation is proposed on the lines of Gervais-Neveu-Felder dynamical quantum algebras. 
Jean Avan, Eric Ragoucy and Vladimir Rubtsov
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