扭Heisenberg-Virasoro代数上的Poisson结构

赵晓晓, 高寿兰, 刘东

数学学报 ›› 2016, Vol. 59 ›› Issue (6) : 775-782.

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数学学报 ›› 2016, Vol. 59 ›› Issue (6) : 775-782. DOI: 10.12386/A2016sxxb0069
论文

扭Heisenberg-Virasoro代数上的Poisson结构

    赵晓晓, 高寿兰, 刘东
作者信息 +

Poisson Structure on the Twisted Heisenberg-Virasoro Algebra

    Xiao Xiao ZHAO, Shou Lan GAO, Dong LIU
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文章历史 +

摘要

Poisson代数是指同时具有代数结构和李代数结构的一类代数,其乘法与李代数乘法满足Leibniz法则.扭Heisenberg-Virasoro代数是一类重要的无限维李代数,是次数不超过1的微分算子李代数W(0)的普遍中心扩张,与曲线的模空间有密切联系.本文主要研究扭Heisenberg-Virasoro代数上的Poisson结构,首先确定了李代数W(0)上的Poisson结构,进而给出了扭Heisenberg-Virasoro代数上的Poisson结构.

Abstract

Poisson algebras are algebras with an algebra structure and a Lie algebra structure, both of which satisfy the Leibniz law. The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra W(0) of differential operators of order at most one, which is connected with certain moduli spaces of curves. This paper mainly determines the Poisson structure of the Lie algebra W(0) as well as the twisted Heisenberg-Virasoro algebra.

关键词

扭Heisenberg-Virasoro代数 / Poisson代数 / Leibniz法则 / Witt代数

Key words

twisted Heisenberg-Virasoro algebra / Poisson algebra / Leibniz rule

引用本文

导出引用
赵晓晓, 高寿兰, 刘东. 扭Heisenberg-Virasoro代数上的Poisson结构. 数学学报, 2016, 59(6): 775-782 https://doi.org/10.12386/A2016sxxb0069
Xiao Xiao ZHAO, Shou Lan GAO, Dong LIU. Poisson Structure on the Twisted Heisenberg-Virasoro Algebra. Acta Mathematica Sinica, Chinese Series, 2016, 59(6): 775-782 https://doi.org/10.12386/A2016sxxb0069

参考文献

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基金

国家自然科学基金资助项目(11371134,11201141);浙江省自然科学基金资助项目(LZ14A010001,LQ12A01005,LY16A010016)

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