We prove that all the Lie bialgebra structures on the one sided Witt algebra W1, on the Witt algebra W and on the Virasoro algebra V are triangular coboundary Lie bialgebra structures associated to skew-symmetric solutions r of the classical Yang-Baxter equation of the form r = a ∧ b. In particular, for the one-sided Witt algebra W1 = Der k[t] over an algebraically closed field k of characteristic zero, the Lie bialgebra structures discovered in Michaelis (Adv. Math. 107 (1994) 365-392) and Taft (J. Pure Appl. Algebra 87 (1993) 301-312) are all the Lie bialgebra structures on W1 up to isomorphism. We prove the analogous result for a class of Lie subalgebras of W which includes W1. © 2000 Elsevier Science B.V. All rights reserved.
Publication Source (Journal or Book title)
Journal of Pure and Applied Algebra
Ng, S., & Taft, E. (2000). Classification of the Lie bialgebra structures on the Witt and Virasoro algebras. Journal of Pure and Applied Algebra, 151 (1), 67-88. https://doi.org/10.1016/S0022-4049(99)00045-6