Conformal Yang–Baxter equation on Cur(sl2(C))

Abstract

In 2008, Liberati [J. Algebra 319, 2295–2318 (2008)] defined what a conformal Lie bialgebra is and introduced the conformal classical Yang–Baxter equation (CCYBE). An L-invariant solution to the weak version of CCYBE provides a conformal Lie bialgebra structure. We describe all solutions to the CCYBE on the current Lie conformal algebra Cur(sl2(C)) and to the weak version of it.