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LIE_ALGEBRA: 作品数：204被引量：163H指数：6; 导出分析报告; 相关作者：管克英雷锦志刘胜周建华朱海星更多>>; 相关机构：东南大学北京航空航天大学华中科技大学烟台师范学院更多>>; 相关期刊：更多>>; 相关基金：国家自然科学基金国家教育部博士点基金上海市教育委员会重点学科基金河北省自然科学基金更多>>

Multiplicative forms on Poisson groupoids: 《Science China Mathematics》2025年第1期169-206,共38页Zhuo Chen Honglei Lang Zhangju Liu; supported by National Natural Science Foundation of China(Grant No.12071241);the National Key Research and Development Program of China(Grant No.2021YFA1002000).; First,we prove a decomposition formula for any multiplicative differential form on a Lie groupoid G.Next,we prove that if G is a Poisson Lie groupoid,then the spaceΩ_(mult)·(G)of multiplicative forms on G has a diff...; 关键词：multiplicative form Poisson groupoid Lie algebra crossed module characteristic pair

Discussion on the Homology Theory of Lie Algebras: 《Journal of Applied Mathematics and Physics》2024年第7期2367-2376,共10页Lilong Kang Yu Wang Caiyu Du; Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent m...; 关键词：Lie Algebra Differential Sequence Differential Fractional Algebra COHOMOLOGY

Structure and Representations for Electrical Lie Algebra of Type D_(5): 《Algebra Colloquium》2024年第2期271-284,共14页Yulu Chen Ran Shen Yucai Su; Supported by the Fundamental Research Funds for the Central Universities(Grant No.2232021G-13).; In this paper,we prove that the electrical Lie algebra e D_(5)is isomorphic to the semidirect product of sp_(4)and a 2-step nilpotent Lie algebra.Furthermore,we classify the irreducible highest weight modules for e D_...; 关键词：electrical Lie algebra 2-step nilpotent Lie algebra highest weight module

Centroid Hom-associative Algebras and Centroid Hom-Lie Algebras: 《Acta Mathematica Sinica,English Series》2024年第4期935-961,共27页Yu Xiu BAI Leonid A.BOKUT Yu Qun CHEN Ze Rui ZHANG; the grant of Guangzhou Civil Aviation College(Grant No.22X0430);the RAS Fundamental Research Program(Grant No.FWNF-2022-0002);the NNSF of China(Grant Nos.11571121,12071156);the NNSF of China(Grant No.12101248);the China Postdoctoral Science Foundation(Grant No.2021M691099)。; In this article,we construct free centroid hom-associative algebras and free centroid hom-Lie algebras.We also construct some other relatively free centroid hom-associative algebras by applying the Gr?bner-Shirshov ba...; 关键词：Centroid hom-Lie algebra centroid hom-associative algebra Gr?bner-Shirshov basis

Embedding Tensors on 3-Hom-Lie Algebras: 《Journal of Mathematical Research with Applications》2024年第2期187-198,共12页Wen TENG Jiulin JIN Yu ZHANG; Supported by the Scientific Research Foundation for Science&Technology Innovation Talent Team of the Intelligent Computing and Monitoring of Guizhou Province(Grant No.QJJ[2023]063);the Science and Technology Program of Guizhou Province(Grant Nos.ZK[2023]025;QKHZC[2023]372;ZK[2022]031);the National Natural Science Foundation of China(Grant No.12161013);the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022KYYB08);the Doctoral Research Start-Up Fund of Guiyang University(Grant No.GYU-KY-2024).; In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie...; 关键词：3-Hom-Lie algebra embedding tensor representation COHOMOLOGY DEFORMATION

Omni-Representations of Leibniz Algebras: 《Communications in Mathematical Research》2024年第1期30-42,共13页Zhangju Liu Yunhe Sheng; supported by the NSFC (Grant No.12071241).; In this paper,first we introduce the notion of an omni-representation of a Leibniz algebra g on a vector space V as a Leibniz algebra homomorphism from g to the omni-Lie algebra gl(V)V.Then we introduce the omnicohomo...; 关键词：Leibniz algebra omni-Lie algebra REPRESENTATION COHOMOLOGY

Infinite-dimensional necklace Lie algebras and some finite-dimensional important subalgebras: 《Frontiers of Mathematics in China》2023年第5期353-365,共13页Demin YU Caihui LU; In this paper,a new infinite-dimensional necklace Lie algebra is studied and the left and right index arrays of a necklace word in necklace Lie algebra is first defined.Using the left and right index arrays,we divide ...; 关键词：Necklace Lie algebra left and right index arrays SUBALGEBRA

COMPARISON OF HOMOLOGIES AND AUTOMATIC EXTENSIONS OF INVARIANT DISTRIBUTIONS: 《Acta Mathematica Scientia》2023年第4期1561-1570,共10页陈阳洋; the Fundamental Research Funds for the Central Universities(JUSRP121045);the NSF of Jiangsu Province(BK20221057)。; Let G be a reductive Nash group,acting on a Nash manifold X.Let Z be a G-stable closed Nash submanifold of X and denote by U the complement of Z in X.Letχbe a character of G and denote by g the complexified Lie algeb...; 关键词：Schwartz functions Lie algebra homology Hausdorffness Schwartz distributions automatic extensions

Maurer-Cartan characterizations and cohomologies of compatible Lie algebras被引量：1: 《Science China Mathematics》2023年第6期1177-1198,共22页Jiefeng Liu Yunhe Sheng Chengming Bai; supported by National Natural Science Foundation of China (Grant Nos.11901501,11922110 and 11931009);supported by the Fundamental Research Funds for the Central Universities;Nankai Zhide Foundation;supported by the National Key Research and Development Program of China (Grant No.2021YFA1002000);the Fundamental Research Funds for the Central Universities (Grant No.2412022QD033)。; In this paper,we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie algebras.Explicitly,we first introduce the notion of a bidifferential graded Lie algebra and thus give Maurer-Car...; 关键词：compatible Lie algebra Maurer-Cartan element COHOMOLOGY deformation EXTENSION

3-Bihom-ρ-Lie Algebras, 3-Pre-Bihom-ρ-Lie Algebras: 《Chinese Annals of Mathematics,Series B》2023年第2期193-208,共16页Zahra BAGHERI Esmaeil PEYGHAN; The purpose is to introduce the notions of 3-Bihom-ρ-Lie algebras and 3-preBihom-ρ-Lie algebras.The authors describe their constructions and express the related lemmas and theorems.Also,they define the 3-Bihom-ρ-Le...; 关键词：3-Bihom-ρ-Lie algebra 3-Pre-Bihom-ρ-Lie algebra Rota-Baxer operator

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