What a Classical r-Matrix Really Is

  title={What a Classical r-Matrix Really Is},
  author={Boris A. Kupershmidt},
  journal={Journal of Nonlinear Mathematical Physics},
  • B. Kupershmidt
  • Published 1 October 1999
  • Mathematics
  • Journal of Nonlinear Mathematical Physics
Abstract To my friend and colleague K.C. Reddy on occasion of his retirement. The notion of classical r-matrix is re-examined, and a definition suitable to differential (-difference) Lie algebras, – where the standard definitions are shown to be deficient, – is proposed, the notion of an O-operator. This notion has all the natural properties one would expect form it, but lacks those which are artifacts of finite-dimensional isomorpisms such as not true in differential generality relation End (V… 
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