# What a Classical r-Matrix Really Is

@article{Kupershmidt1999WhatAC,
title={What a Classical r-Matrix Really Is},
author={Boris A. Kupershmidt},
journal={Journal of Nonlinear Mathematical Physics},
year={1999},
volume={6},
pages={448-488}
}
• 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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