3-李代数的辛结构

白瑞蒲, 陈双双, 程荣

数学学报 ›› 2016, Vol. 59 ›› Issue (5) : 711-720.

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数学学报 ›› 2016, Vol. 59 ›› Issue (5) : 711-720. DOI: 10.12386/A2016sxxb0063
论文

3-李代数的辛结构

    白瑞蒲, 陈双双, 程荣
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Symplectic Structures on 3-Lie Algebras

    Rui Pu BAI, Shuang Shuang, CHEN Rong CHENG
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摘要

研究了3-李代数和度量3-李代数的辛结构.对任意3-李代数L,构造了无限多个度量辛3-李代数.证明了度量3-李代数(A,B)是度量辛3-李代数的充要条件,即存在可逆导子D,使得D∈DerBA).同时证明了每一个度量辛3-李代数(Ã,)是度量辛3-李代数(A,B,ω)的Tθ*-扩张.最后,利用度量辛3-李代数经过特殊导子的双扩张得到了新的度量辛3-李代数.

Abstract

The symplectic structures on 3-Lie algebras and metric symplectic 3-Lie algebras are studied. For arbitrary 3-Lie algebra L, infinite many metric symplectic 3-Lie algebras are constructed. It is proved that a metric 3-Lie algebra (A,B) is a metric symplectic 3-Lie algebra if and only if there exists an invertible derivation D such that D∈DerB(A), and is also proved that every metric symplectic 3-Lie algebra (Ã,) is a Tθ*-extension of a metric symplectic 3-Lie algebra (A,B,ω). Finally, we construct a metric symplectic double extension of a metric symplectic 3-Lie algebra by means of a special derivation.

关键词

3-李代数 / 度量3-李代数 / 辛3-李代数 / Tθ*-扩张

Key words

3-Lie algebra / metric 3-Lie algebra / symplectic 3-Lie algebra / Tθ*-extension

引用本文

导出引用
白瑞蒲, 陈双双, 程荣. 3-李代数的辛结构. 数学学报, 2016, 59(5): 711-720 https://doi.org/10.12386/A2016sxxb0063
Rui Pu BAI, Shuang Shuang, CHEN Rong CHENG. Symplectic Structures on 3-Lie Algebras. Acta Mathematica Sinica, Chinese Series, 2016, 59(5): 711-720 https://doi.org/10.12386/A2016sxxb0063

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基金

国家自然科学基金资助项目(11371245);河北省自然科学基金资助项目(A2014201006)

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