Abstract
Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of ad L. For generic L a generalized inverse (and indeed the Moore - Penrose inverse) is explicitly constructed. The R-matrices are, in general, momentum dependent and dynamical. The construction applies equally to Lax matrices with spectral parameter.
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