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Tensor solutions ($r$-matrices) of the classical Yang-Baxter equation (CYBE)in a Lie algebra, obtained as the classical limit of the $R$-matrix solution ofthe quantum Yang-Baxter equation (QYBE), is an important structure appearing indifferent areas such as integrable systems, symplectic geometry, quantum groupsand quantum field theory. Further study of CYBE led to its interpretation ascertain operators, giving rise to the concept of O-operators. In [3], theO-operators were in turn interpreted as tensor solutions of CYBE by enlargingthe Lie algebra. The purpose of this paper is to extend this study to a moregeneral class of operators that were recently introduced [4] in the study ofLax pairs in integrable systems. Relationship between $\calo$-operators,relative differential operators and Rota-Baxter operators are also discussed.

Generalizations of the classical Yang-Baxter equation and O-operators