共查询到17条相似文献,搜索用时 46 毫秒
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Hamiltonian type Lie bialgebras 总被引:2,自引:0,他引:2
Bin XIN~ 《中国科学A辑(英文版)》2007,50(9):1267-1279
We first prove that,for any generalized Hamiltonian type Lie algebra H,the first co- homology group H~1(H,H(?)H) is trivial.We then show that all Lie bialgebra structures on H are triangular. 相似文献
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LiangYun Zhang 《中国科学A辑(英文版)》2008,51(6):1017-1026
In this paper,we first give a direct sum decomposition of Lie comodules,and then accord- ing to the Lie comodule theory,construct some(triangular)Lie bialgebras through Lie coalgebras. 相似文献
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J. Abedi-Fardad A. Rezaei-Aghdam Gh. Haghighatdoost 《Theoretical and Mathematical Physics》2017,190(1):1-17
We classify all four-dimensional real Lie bialgebras of symplectic type and obtain the classical r-matrices for these Lie bialgebras and Poisson structures on all the associated four-dimensional Poisson–Lie groups. We obtain some new integrable models where a Poisson–Lie group plays the role of the phase space and its dual Lie group plays the role of the symmetry group of the system. 相似文献
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We consider a class of generalized Kuznetsov–Zabolotskaya–Khokhlov (gKZK) equations and determine its equivalence group, which is then used to give a complete symmetry classification of this class. The infinite-dimensional symmetry is used to reduce such equations to (1+1)-dimensional PDEs. Special attention is paid to group-theoretical properties of a class of generalized dispersionless KP (gdKP) or Zabolotskaya–Khokhlov equations as a subclass of gKZK equations. The conditions are determined under which a gdKP equation is invariant under a Lie algebra containing the Virasoro algebra as a subalgebra. This occurs if and only if this equation is completely integrable. A similar connection is shown to hold for generalized KP equations. 相似文献
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Daniel Beltiţă Tomasz Goliński Grzegorz Jakimowicz Fernand Pelletier 《Journal of Functional Analysis》2019,276(5):1528-1574
We study a few basic properties of Banach–Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theory, we show that the notion of locally transitive Banach–Lie groupoid sheds fresh light on earlier research on some infinite-dimensional manifolds associated with Banach algebras. 相似文献
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Derivations and structure of the Lie algebras¶of Xu type 总被引:3,自引:0,他引:3
Yucai Su 《manuscripta mathematica》2001,105(4):483-500
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We study some properties of generalized reduced Verma modules over ?-graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and coinduced modules are obtained. Moreover, invariant forms on the generalized reduced Verma modules are considered. In particular, for ?-graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules. 相似文献
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In an article by Michaelis, a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In a recent article by Song and Su, Lie bialgebra structures on graded Lie algebras of generalized Witt type with finite dimensional homogeneous components were considered. In this article we consider Lie bialgebra structures on the graded Lie algebras of generalized Witt type with infinite dimensional homogeneous components. By proving that the first cohomology group H1(𝒲, 𝒲 ? 𝒲) is trivial for any graded Lie algebras 𝒲 of generalized Witt type with infinite dimensional homogeneous components, we obtain that all such Lie bialgebras are triangular coboundary. 相似文献
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Lie bialgebra structures on Lie algebras of generalized Weyl type are studied. They are shown to be triangular coboundary. 相似文献
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Lie Bialgebras of a Family of Lie Algebras of Block Type 总被引:2,自引:0,他引:2
Lie bialgebra structures on a family of Lie algebras of Block type are shown to be triangular coboundary. 相似文献
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The article contains an explicit formula for the restricted Lie algebra structure in the Witt Lie algebra over a field of finite characteristic. Some combinatorial lemmas can be of independent interest. 相似文献
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This paper is a continuation of [EK]. We show that the quantization procedure of [EK] is given by universal acyclic formulas
and defines a functor from the category of Lie bialgebras to the category of quantized universal enveloping algebras. We
also show that this functor defines an equivalence between the category of Lie bialgebras over k [[h]] and the category of quantized universal enveloping (QUE) algebras. 相似文献
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