| Central simple Poisson algebras |
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| 作者姓名： | SU Yucai & XU Xiaoping |
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| 作者单位： | SU Yucai & XU Xiaoping
Department of Mathematics，Shanghai Jiaotong University，Shanghai 200030，China;
Institute of Mathematics，Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | 国家自然科学基金，教育部优秀青年教师资助计划 |
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| 摘 要： | Poisson algebras are fundamental algebraic structures in physics and sym-plectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
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Central simple Poisson algebras |
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| SU Yucai & XU Xiaoping.Central simple Poisson algebras[J].Science in China(Mathematics),2004,47(2):245-263. |
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| Authors: | Yucai Su Xiaoping Xu |
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| Institution: | 1. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China
2. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences,Beijing 100080, China |
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| Abstract: | Poisson algebras are fundamental algebraic structures in physics and sym-plectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero. The Lie algebra structures of these Poisson algebras are in general not finitely-graded. |
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| Keywords: | Poisson algebra locally-finite operator derivation finitely-graded isomorphism class |
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