Classification of the Lie bialgebra structures on the Witt and Virasoro algebras (Q1577500)

Let \(k\) be a field of characteristic zero and let \(W\) be the Witt algebra over \(k\), which can be identified with the Lie algebra of derivations of the Laurent polynomial algebra \(k[t,t^{-1}]\). The one-sided Witt algebra \(W_1\) is the Lie algebra of derivations on the polynomial algebra \(k[t]\). The Virasoro algebra \(V\) is a certain central extension of \(W\). The authors prove that any Lie bialgebra structure on \(W_1\), \(W\) or \(V\) is a triangular coboundary Lie bialgebra structure associated to a skew-symmetric solution \(r\) of the classical Yang-Baxter equation of the form \(r=a\wedge b\).