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Constructions of Metric (n+1)-Lie Algebras

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Chinese Annals of Mathematics,Series B 2016年第5期37卷 729-742页

作者： ruipu bai Shuangshuang CHEN College of Mathematics and Information Science Hebei University

Metric n-Lie algebras have wide applications in mathematics and mathematical physics. In this paper, the authors introduce two methods to construct metric (n+1)-Lie algebras from metric n-Lie algebras for n≥2. For a given m-dimensional metric n-Lie algebra(g, [, ···, ], B_g), via one and two dimensional extensions ￡=g+IFc and g0= g+IFx^(-1)+IFx^0 of the vector space g and a certain linear function f on g, we construct(m+1)-and (m+2)-dimensional (n+1)-Lie algebras(￡, [, ···, ]cf) and(g0, [, ···, ]1), ***, if the center Z(g) is non-isotropic, then we obtain metric(n + 1)-Lie algebras(L, [, ···, ]cf, B) and(g0, [, ···, ]1, B) which satisfy B|g×g = Bg. Following this approach the extensions of all(n + 2)-dimensional metric n-Lie algebras are discussed.

关键词： algebra extensions mathematics satisfy multiplication commutative degenerate Cartan bilinear isotropic

3-Lie Algebras Realized by Cubic Matrices

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Chinese Annals of Mathematics,Series B 2014年第2期35卷 261-270页

作者： ruipu bai Hui LIU Meng ZHANG College of Mathematics and Computer Science Hebei University

Associative multiplications of cubic matrices are *** N3-dimensional3-Lie algebras are realized by cubic matrices,and structures of the 3-Lie algebras are studied.

关键词： 3-Lie algebra Cubic matrix Multiplication

Infinite-dimensional 3-Lie algebras and their ：onnections to Harish-Chandra modules

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Frontiers of Mathematics in China 2017年第3期12卷 515-530页

作者： ruipu bai Zhenheng LI Weidong WANG College of Mathematics and Information Science Hebei University Baoding 071002 China Department of Mathematical Sciences University of South Carolina Aiken Aiken SC 29801 USA

We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation algebras. In particular, for the second kind of 3-Lie algebras, we find that their regular representations are Harish-Chandra modules, and the inner derivation algebras give rise to intermediate series modules of the Witt algebras and contain the smallest full toroidal Lie algebras without center.

关键词： 3-Lie algebra Harish-Chandra module Witt algebra intermediate series module toroidal Lie algebra inner derivation algebra

q-Deformations of 3-Lie Algebras

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Algebra Colloquium 2017年第3期24卷 519-540页

作者： ruipu bai Lixin Lin Yan Zhang Chuangchuang Kang College of Mathematics and Information Science Hebei University Baoding Hebei 071002 China

q-Deformations of 3-Lie algebras and representations of q-3-Lie algebras are discussed. A q-3-Lie algebra （A, [, ,]q, [, ,]＇q, Ja）, where q ∈ F and q ≠ 0, is a vector space A over a field F with 3-cry linear multiplications [,, ]q and [,, ]＇q from A 3 to A, and a map Jq ： A 5→ F satisfying the q-Jacobi identity Jq（x1, x2, x3, x4, x5）[x1, x2, [x3, x4, x5]q]＇q = Jq（x4, x5, x1, x2, x3）[x4, x5, [x1, x2, x3]q]＇q for all x1 ∈ A. If the multiplications satisfy that [,,]q = [,,]＇q and [,,]q is skew-symmetry, then （A, [,,]q, Jq） is called a type （I）-q-3- Lie algebra. From q-Lie algebras, group algebras and commutative associative algebras, q-3-Lie algebras and type （I）-q-3-Lie algebras are constructed. Also, the non-trivial one- dimensional central extension of q-3-Lie algebras is investigated, and new q-3-Lie algebras （DerqC[x,x-1], [, ,]q, [, ,]＇q, Jq）, and （Derδq C[x,x-1], [, ,]q, [,,]＇q, Jq） are obtained.

关键词： q-3-Lie algebra q-deformation q-Jacobi identity

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3-LIE BIALGEBRAS

Acta Mathematica Scientia 2014年第2期34卷 513-522页

作者：白瑞蒲程宇李佳倩孟伟 College of Mathematics and Computer Science Hebei University Department of Mathematics Baoding University

3-Lie algebras have close relationships with many important fields in mathemat- ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char- acteristic zero are provided.

关键词： 3-Lie algebra 3-Lie coalgebra 3-Lie bialgebra

n-李代数的Jordan Holder定理与饱和态像

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数学物理学报（A辑） 2008年第6期28卷 1015-1022页

作者：白瑞蒲河北大学数学与计算机学院

该文证明了n-李代数的Jordan-Holder定理,并对n-李代数的饱和态像进行系统的研究.

关键词： n-李代数态像列队饱和态像

The Cobordism Classification of Involution on DOLD Manifold P(1,2l)

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Acta Mathematica Sinica,English Series 1997年第1期13卷 9-20页

作者： Wu Zhende Liu Zongze (Department of Mathematics,Hebei Normal University,Shijazhuang 050016,China)bai ruipu (Department of Mathematics,Hebei University,Baoding 071002,China) Department of Mathematics Hebei Normal University Department of Mathematics Hebei University

Supposing the smooth involution of the DOLD manifold P(2,2l)satisfies the following condition:the fiberation π:P(1,2l)×T_×(-1)S~∞→RP(∞)is totally nonhomologous to zero(cf.[1, p373]),this paper determines the cla... 详细信息

关键词： Stiefel-Whitney class Involution on smooth manifold Bordism class Wu formulas

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(n-1)-半单的n-李代数的几何描述

应用数学学报 2010年第6期33卷 1087-1094页

作者：白瑞蒲程宇河北大学数学与计算机学院保定071002 保定学院数学系保定071002

证明了实数域上(n-1)-半单的(n+1)维n-李代数A是n维欧氏空间的Lorentz群O(p,n-p)与n维Abel正规子群的半直积的n-李代数.且当p=0时,A是n维欧氏空间的等距变换群的n-李代数.并提出了关于(n-1)-半单的(n+1)维n-李代数的外导子的物理应用与... 详细信息

证明了实数域上(n-1)-半单的(n+1)维n-李代数A是n维欧氏空间的Lorentz群O(p,n-p)与n维Abel正规子群的半直积的n-李代数.且当p=0时,A是n维欧氏空间的等距变换群的n-李代数.并提出了关于(n-1)-半单的(n+1)维n-李代数的外导子的物理应用与几何应用问题.

关键词： n-李代数李群等距变换群

无限维齐性Rota-Baxter 3-李代数(Ⅱ)

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河北大学学报（自然科学版） 2022年第4期42卷 343-349页

作者：白瑞蒲刘山河北大学数学与信息科学学院河北保定071002

利用无限维单3-李代数A_(ω)上权为1且满足g(0)+g(1)+1=0的齐性Rota-Baxter算子R_(k),构造了13类齐性Rota-Baxter 3-李代数A_(k),1≤k≤13,证明了在齐性Rota-Baxter 3-李代数A_(k)中存在5类两两不同构的齐性Rota-Baxter 3-李代数D_(i),... 详细信息

关键词： 3-李代数 Rota-Baxter算子齐性Rota-Baxter 3-李代数