Journal of Lie Theory 21 (2011), No. 1, 101--122
Copyright Heldermann Verlag 2011
Structure of the Local Area-Preserving 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 infinite-dimensional Lie algebra B, called local area-preserving algebra for the Klein bottle introduced by C. Pope and L. Romans [Class. Quantum Grav. 7 (1990) 79--109]. 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
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