n-李双代数

发布时间：2018-04-28 15:11

本文选题：n-李代数 + n-李双代数　；参考：《河北大学》2017年硕士论文

【摘要】：本文主要研究n-李双代数的结构及其扩张问题.n-李双代数是既具有n-李代数结构,又具有n-李上代数结构的n-元代数结构.因此,为了定义n-李双代数,首先定义了n-李上代数,并利用结构常数研究了 n-李上代数的结构.证明了(L,△)是n-李上代数当且仅当其对偶代数(L*,△*)是n-李代数.且给出了两个n-李上代数(L1,△1)与(L2,△2)同构的充分必要条件.利用结构常数研究了n-李双代数的结构.根据n-李代数和n-李上代数的相容性条件证明了三元有序偶(L,μ,△)为n-李双代数当且仅当其对偶三元有序偶(L*,△*,μ*)是n-李双代数.并且举例说明了在同一个n-李代数(L,μ)的结构上可以构造出不同构的nn-李双代数.对任意一个m-维n-李双代数(L,μ,△),通过对空间进行二维扩张,构造了(m + 2)-维(n + 1)-李双代数(L,μ,△),并对其结构进行了研究.
[Abstract]:In this paper, we mainly study the structure and extension of n-lie bialgebras. N-lie bialgebras are n- element algebraic structures with both n-lie algebraic structures and n-lie upper algebraic structures. Therefore, in order to define n-lie bialgebras, we first define n-lie upper algebras, and study the structure of n-lie upper algebras by using structural constants. It is proved that L,) is a n-lie upper algebra if and only if its dual algebra is n lie algebra. The sufficient and necessary conditions for the isomorphism of two n- lie upper algebras L _ 1, 1) and L _ 2, 2) are also given. The structure of n-lie bialgebra is studied by using structure constant. According to the compatibility conditions of n-lie algebras and n-lie upper algebras, it is proved that ternary ordered dialgebras L, 渭,) are n-lie bialgebras if and only if their dual ternary ordered dialgebras are n-lie bialgebras. An example is given to show that nn-lie bialgebras with different structures can be constructed on the same n-lie algebra L, 渭). In this paper, we construct a m2-dimensional n-lie bialgebra L, 渭, L, and study its structure by extending the space into two dimensions.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152.5

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