Journal of Lie Theory

no. 1
Structure of the Local Area-Preserving Lie Algebra for the Klein Bottle
Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 101-122
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.
DOI: 10.5802/jolt.625
Classification: 17B65, 17B68
Keywords: Lie algebra, Klein bottle, Invariant bilinear form, central extension, derivation 
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     author = {C. Jiang and J. Jiang and Y. Pei},
     title = {Structure of the {Local} {Area-Preserving} {Lie} {Algebra} for the {Klein} {Bottle}},
     journal = {Journal of Lie Theory},
     pages = {101--122},
     year = {2011},
     volume = {21},
     number = {1},
     doi = {10.5802/jolt.625},
     zbl = {1253.17014},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.625/}
}
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C. Jiang; J. Jiang; Y. Pei. Structure of the Local Area-Preserving Lie Algebra for the Klein Bottle. Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 101-122. doi: 10.5802/jolt.625

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