
Journal of Lie Theory 21 (2011), No. 1, 101122 Copyright Heldermann Verlag 2011 Structure of the Local AreaPreserving Lie Algebra for the Klein Bottle Cuipo Jiang Dept. of Mathematics, Shanghai Jiaotong University, No. 800 Dongchuan Road, Shanghai, P.R.China 200240 cpjiang@sjtu.edu.cn Jingjing Jiang Dept. of Mathematics, Shanghai Jiaotong University, No. 800 Dongchuan Road, Shanghai, P.R.China 200240 jingjingjiang@sjtu.edu.cn Yufeng Pei Dept. of Mathematics, Shanghai Normal University, No. 100 Guilin Road, Shanghai, P.R.China 200234 peiyufeng@gmail.com We study an infinitedimensional Lie algebra B, called local areapreserving algebra for the Klein bottle introduced by C. Pope and L. Romans [Class. Quantum Grav. 7 (1990) 79109]. We show that B is a finitely generated simple Lie algebra with a unique (up to scalars) symmetric invariant bilinear form. The derivation algebra and the universal central extension of B are also determined. Keywords: Lie algebra, Klein bottle, Invariant bilinear form, central extension, derivation. MSC: 17B65, 17B68 [ Fulltextpdf (204 KB)] for subscribers only. 