Deformations of the classical \(W\)-algebras associated to \(D_n\), \(E_6\) and \(G_2\) (Q1127725)

Let \(\mathfrak{g}\) denote a Lie algebra of type \(D_n\), \(E_6\) or \(G_2\). The author gives explicit formulae for the generators of the \(q\)-deformed Heisenberg-Poisson algebra \(H_q(\mathfrak{g})\) associated to \(\mathfrak{g}\) and computes the Poisson brackets between them. He also constructs the generators of the \(q\)-deformed \(W\)-algebra \(W_q(\mathfrak{g})\) in such a way that they coincide with the corresponding formulae for the eigenvalues of the transfer-matrices and computes the Poisson brackets between these generators.