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central extension for the Triangular Derivation Lie Algebra

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Journal of Mathematical Research with Applications 2012年第5期32卷 561-570页

作者： Chunming LI,Ping XU Department of Mathematics,Heilongjiang University,Heilongjiang 150090,P.R.China Department of Mathematics Heilongjiang University Heilongjiang 150090

In this paper,we study a class of subalgebras of the Lie algebra of vector fields on n-dimensional torus,which are called the Triangular derivation Lie algebra.We give the structure and the central extension of Triang... 详细信息

关键词： triangular derivation Lie algebra central extension 2-cocycle.

The central extension of an Elementary Abelian p-Group by a Miniaml Non-Abelian p-Group

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Journal of Mathematical Research with Applications 2016年第4期36卷 457-466页

作者： Lijian AN Le YANG Department of Mathematics Shanxi Normal University

Assume that N, F and G are groups. If there exsits a normal subgroup of G such that≌ G and G/≌ F, then G is called a central extension of N by F. In this paper, the central extension of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group of order p;. Together with our previous work, all central extensions of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group.

关键词： central extension minimal non-abelian p-groups congruent

One-Generated Nilpotent Bicommutative Algebras

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Algebra Colloquium 2022年第3期29卷 453-474页

作者： Ivan Kaygorodov Pilar Páez-Guillán Vasily Voronin Centro de Matemática e Aplicacōes Universidade da Beira InteriorCovilhãPortugal Institute of Mathematics and Mathematical ModelingAlmatyKazakhstan University of Santiago de Compostela Santiago de CompostelaSpain University of ViennaViennaAustria Novosibirsk State University NovosibirskRussia

We give a classification of 5-and 6-dimensional complex one-generated nilpotent bicommutative algebras.

关键词： bicommutative algebras nilpotent algebras algebraic classification central extension

central extensions and Deformations of Lie Triple Systems with a Derivation

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Journal of Mathematical Research with Applications 2022年第2期42卷 189-198页

作者： Shuangjian GUO School of Mathematics and Statistics Guizhou University of Finance and Economics

In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with coefficients in a representation. We study central extensions of a LietsDer pair. In the next, we generalize the formal deformation theory to LietsDer pairs in which we deform both the Lie triple system bracket and the distinguished derivation. It is governed by the cohomology of LietsDer pair with coefficients in itself.

关键词： Lie triple system derivation representation cohomology central extension deformation

Finite 2-groups whose nonnormal subgroups have orders at most 2^3

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Frontiers of Mathematics in China 2012年第5期7卷 971-1003页

作者： Qinhai ZHANG Meijuan SU Department of Mathematics Shanxi Normal UniversityLinfen 041004China

In this paper, we classify finite 2-groups all of whose nonnormal subgroups have orders at most 2^3. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of P... 详细信息

关键词： Minimal non-abelian p-group nonnormal subgroup central extension

q-Deformation of W (2 , 2) Lie Algebra Associated with Quantum Groups

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Acta Mathematica Sinica,English Series 2012年第11期28卷 2213-2226页

作者： La Mei YUAN Academy of Fundamental and Interdisciplinary Sciences Harbin Institute of Technology Wu Wen-Tsun Key Laboratory of Mathematics University of Science and Technology of China

The q-deformation of W（2, 2） Lie algebra is well defined based on a realization of this Lie algebra by using the famous bosonic and fermionic oscillators in physics. Furthermore, the quantum group structures on the q-deformation of W（2, 2） Lie algebra are completely determined. Finally, the 1-dimensional central extension of the q-deformed W（2, 2） Lie algebra is studied, which turns out to be coincided with the conventional W（2, 2） Lie algebra in the q → 1 limit.

关键词： W（2 2） Lie algebra q-deformation quantum group central extension

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The q-Analog Klein Bottle Lie Algebra

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Algebra Colloquium 2014年第4期21卷 561-574页

作者： Cuipo Jiang Jingjing Jiang Yufeng Pei Department of Mathematics Shanghai diaotong UniversityShanghai 200240 China Department of Mathematics Shanghai Normal University Shanghai 200234 China

In this paper, we study an infinite-dimensional Lie algebra Bq, called the q-analog Klein bottle Lie algebra. We show that Bq is a finitely generated simple Lie algebra with a unique （up to scalars） symmetric invari... 详细信息

关键词： Lie algebra Klein bottle invariant bilinear form central extension derivation

Finitely Generated Nilpotent Groups of Infinite Cyclic Commutator Subgroups

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Acta Mathematica Sinica,English Series 2020年第12期36卷 1315-1340页

作者： Jun LIAO He Guo LIU Xing Zhong XU Ji Ping ZHANG Hubei Key Laboratory of Applied Mathematics School of Mathematics and StatisticsHubei UniversityWuhan 430062P.R.China School of Mathematical Sciences Peking UniversityBeijing 100871P.R.China

The aim of this paper is to determine the structure and to establish the isomorphic invariant of the finitely generated nilpotent group G of infinite cyclic commutator subgroup.Using the structure and invariant of the group which is the central extension of a cyclic group by a free abelian group offinite rank of infinite cyclic center,we provide a decomposition of G as the product of a generalized extraspecial Z-group and its center.By using techniques of lifting isomorphisms of abelian groups and equivalent normal form of the generalized extraspecial Z-groups,we finally obtain the structure and invariants of the group G.

关键词： Nilpotent groups central extension isomorphic invariant

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Structure of a Class of Rank Two Lie Conformal Algebras

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Algebra Colloquium 2021年第1期28卷 169-180页

作者： Wei Wang Chunguang Xia School of Mathematics and Statistics Ningxia UniversityYinchuan 750021China School of Mathematics China University of Mining and TechnologyXuzhouJiangsu 221116China

Letβbe a complex number,and a class of non-semisimple and non-solvable rank two Lie conformal algebras L(β)are introduced.In this paper,conformal derivations,conformal quasiderivations,generalized conformal derivations and conformal biderivations of L(β)are studied.Besides,central extensions and conformal modules of rank one of L(β)are determined.

关键词： conformal derivation central extension conformal module