Journal of Lie Theory 19 (2009), No. 4, 639--659
Copyright Heldermann Verlag 2009
Lie Bialgebras on k3 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 k3 and the corresponding Lagrange varieties are classified by means of a pair of quadratic forms on k4, 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 kP3 defined by the above quadratic forms respectively.
Keywords: Lie bialgebra, Lagrange subalgebra.
MSC: 17B62, 17B66, 53D17
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