R-Matrices and Generalized Inverses

Details R-Matrices and Generalized Inverses R-Matrices and Generalized Inverses

1997-05-30

arxiv.org/abs/solv-int/9706001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, Latex

Scientific paper

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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