
Journal of Lie Theory 19 (2009), No. 4, 639659 Copyright Heldermann Verlag 2009 Lie Bialgebras on k^{3} and Lagrange Varieties Wei Hong Dept. of Mathematics and LMAM, Beijing University, Beijing 100871, China hongweimath@pku.edu.cn Zhangju Liu Dept. of Mathematics and LMAM, Beijing University, Beijing 100871, China liuzj@pku.edu.cn Lie bialgebras on k^{3} and the corresponding Lagrange varieties are classified by means of a pair of quadratic forms on k^{4}, where k is a field whose characteristic is not 2. It turns out that any Lagrange variety is composed of two (possibly degenerate) quadratic surfaces in kP_{3} defined by the above quadratic forms respectively. Keywords: Lie bialgebra, Lagrange subalgebra. MSC: 17B62, 17B66, 53D17 [ Fulltextpdf (248 KB)] for subscribers only. 