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Extension of a quantized enveloping algebra by a Hopf algebra

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Science China Mathematics 2010年第5期53卷 300-307页

作者： WU ZhiXiang Department of Mathematics,Zhejiang University,Hangzhou 310027,China Department of Mathematics Zhejiang University Hangzhou China

Suppose that H is a Hopf algebra,and g is a generalized Kac-Moody algebra with Cartan matrix A =(aij)I×I,where I is an index set and is equal to either {1,2,...,n} or the natural number set *** f,g be two mappings from I to G(H),the set of group-like elements of H,such that the multiplication of elements in the set {f(i),g(i)|i ∈I} is *** we define a Hopf algebra Hgf Uq(g),where Uq(g) is the quantized enveloping algebra of g.

关键词： quantum enveloping algebra Hopf algebra Kac-Moody algebra

enveloping Lie Algebras of Low Dimensional Leibniz Algebras

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Applied Mathematics 2011年第8期2卷 1027-1030页

作者： Massoud Amini Isamiddin Rakhimov Seyed Jalal Langari 不详

We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in some cases. These results could be used to associate geometric objects (loop spaces) to low dimensional Leibniz algebras.

关键词： Leibniz Algebra enveloping Lie Algebra Nilpotent Algebra

Gear geometry of cycloid drives

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Science China(Technological Sciences) 2008年第5期51卷 598-610页

作者： CHEN BingKui FANG TingTing LI ChaoYang WANG ShuYan State Key Laboratory of Mechanical Transmission Chongqing UniversityChongqing 400044China

According to differential geometry and gear geometry, the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion. The correct meshing condition, contact line, contact ratio, calculating method for pin tooth's maximum contact point are developed. Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1, 2, 3 and ?1, respectively. A general method called enveloping method to generate hypocycloid and epicycloid is put forward. The correct meshing condition for cycloid pin wheel gearing is provided, and the contact line and the contact ratio are also discussed.

关键词： pin wheel cycloid conjugated profile equation of meshing enveloping method contact ratio contact line

Hochschild cohomology of truncated basic cycle

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Science China Mathematics 1997年第12期40卷 1272-1278页

作者：章璞 Department of Mathematics University of Science and Technology of ChinaHefei 230026China

Dimensions of the Hochschild cohomology groups of a truncated algebra of a basic cycle are explicitly given.

关键词： Hochschild cohomology quiver enveloping algebra dimension.

q-DEFORMED VERMA REPRESENTATIONS OF QUANTUM ALGEBRA sl_q(3)AND NEW TYPE YANG-BAXTER MATRICES

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Science China Mathematics 1991年第12期34卷 1474-1483页

作者：孙昌璞吕景发葛墨林 Physics Department Northeast Normal University Changchun 130024 and Theoretical Physics Division Nankai Institute of Mathematics Nankai University Tianjin 300071 PRC Theoretical Physics Division Nankai Institute of Mathematics Nankai University Tianjin 300071 PRC

The q-deformation of Verma theory for the Lie algebra is studied in this paper. Theindecomposable representations and the induced representations of quantum universal envelop-ing algebra sl_q(3) are constructed on the q-deformed Verma space and the quotient spacesrespectively. We put stress on the discussion of the case in which q is a root of unity. Usingthe new representation constrained in the subalgebra sl_q(2), we systematically constructthe new series of solutions (Yang-Baxter matrices) for Yang-Baxter equation without spectralparameter.

关键词： quantum universal enveloping algebra Verma module indecomposable representation Yang-Baxter equation.

On Some Properties of the Heisenberg Laplacian

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Advances in Pure Mathematics 2012年第5期2卷 354-357页

作者： M. E. Egwe Department of Mathematics Universty of Ibadan

Let IHn be the (2n+1) -dimensional Heisenberg group and let Lα and be the sublaplacian and central element of the Lie algebra of IHn respectively. Forα=0 denote by L0=L the Heisenberg Laplacian and let K ∈Aut(IHn) be a compact subgroup of Au-tomorphism of IHn. In this paper, we give some properties of the Heisenberg Laplacian and prove that L and T generate the K-invariant universal enveloping algebra, U(hn)k of IHn.

关键词： Heisenberg Group Heisenberg Laplacian Factorization Universal enveloping Algebra Solvability