李代数上的非交换Poisson代数结构

佟洁;靳全勤;

数学学报 ›› 2009 ›› Issue (01) : 19-34.

数学学报 ›› 2009 ›› Issue (01) : 19-34. DOI: 10.12386/A2009sxxb0003
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李代数上的非交换Poisson代数结构

    佟洁;靳全勤;
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Non-Commutative Poisson Algebra Structures on Lie Algebra ■

    Jie TONT Department of Mathematics and Physics,Shanghai University of Electric Power Shanghai 200090,P.R.China Quan Qin JIN Department of Mathematics,Tongji University,Shanghai 200092,P.R.China
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摘要

非交换的Poisson代数同时具有(未必交换的)结合代数和李代数两种代数结构,且结合代数和李代数之间满足所谓的Leibniz法则.确定了李代数■上所有的Poisson代数结构.

Abstract

Non-commutative Poisson algebras are the algebras having both an asso- ciative algebra structure and a Lie algebra structure together with the Leibniz law.In this paper the non-commutative Poisson algebra structures on ■ are determined.

关键词

广义仿射李代数 / Poisson代数 / Leibniz法则

Key words

Poisson algebra / extended affine Lie algebra / Leibniz law

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佟洁;靳全勤;. 李代数上的非交换Poisson代数结构. 数学学报, 2009(01): 19-34 https://doi.org/10.12386/A2009sxxb0003
Jie TONT Department of Mathematics and Physics,Shanghai University of Electric Power Shanghai 200090,P.R.China Quan Qin JIN Department of Mathematics,Tongji University,Shanghai 200092,P.R.China. Non-Commutative Poisson Algebra Structures on Lie Algebra ■. Acta Mathematica Sinica, Chinese Series, 2009(01): 19-34 https://doi.org/10.12386/A2009sxxb0003

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