共查询到18条相似文献,搜索用时 78 毫秒
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本文详细讨论了李双代数胚中的Dirac结构、群胚上的Dirac结构。利用Dirac结构的特征对的概念,给出了作用不变Dirac结构,拉回Dirac结构等概念的新的刻画。最后利用Dirac结构的有关性质,讨论了泊松齐性空间和泊松群胚作用的约化。 相似文献
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定义了纤维丛的相配群胚的概念,从作用的角度研究了李群胚与主丛的关系;给出了一个泊松群胚在泊松流形上的作用是泊松作用的充要条件;文末得到了一些关于泊松流形上Casimir函数的结果. 相似文献
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从泊松作用的角度考察了群胚上的半直积结构,定义了泊松群胚对泊松群胚的泊松作用,讨论了其性质,并证明了两个泊松群胚的半直积仍是泊松群胚,从而对群胚的半直积结构有了更多的认识. 相似文献
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《数学的实践与认识》2013,(20)
研究了辛群胚与泊松群胚的作用.利用李群胚作用及相关性质,得到了李群胚作用成为辛群胚和泊松群胚作用的充要条件,推广了辛群胚和泊松群胚的性质,为辛群胚与泊松群胚理论的进一步研究起到了推动作用. 相似文献
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关于泊松群胚的余迷向双截面 总被引:3,自引:0,他引:3
令(Г→→P,α,β)是泊松群胚(Poisson groupoid)。本文首先证明了一个关于Г中余迷向双截面(coisotropic bisection)在 性定理,其次证明了,若K是Г泊松同构,利用这一结果进而可以得到有关余迷向双截面的一些性质和一个双截面是余迷和的充分必要条件。 相似文献
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三角Jacobi双代数胚是Mackenzie,徐平所定义的三角李双代数胚的推广.本文将讨论三角Jacobi双代数胚的一些性质,并利用Nijenhuis张量使之成为形变的Jacobi双代数胚.从而可以得到一个Jacobi-Nijenhuis流形. 相似文献
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《Indagationes Mathematicae》2022,33(3):682-717
Motivated by a search for Lie group structures on groups of Poisson diffeomorphisms, we investigate linearizability of Poisson structures of Poisson groupoids around the unit section. After extending the Lagrangian neighbourhood theorem to the setting of cosymplectic Lie algebroids, we establish that dual integrations of triangular bialgebroids are always linearizable. Additionally, we show that the (non-dual) integration of a triangular Lie bialgebroid is linearizable whenever the -matrix is of so-called cosymplectic type. The proof relies on the integration of a triangular Lie bialgebroid to a symplectic LA-groupoid, and in the process we define interesting new examples of double Lie algebroids and LA-groupoids. We also show that the product Poisson groupoid can only be linearizable when the Poisson structure on the unit space is regular. 相似文献
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Qi Lin Yang 《数学学报(英文版)》2002,18(2):301-310
We establish the concept of a quotient affine Poisson group, and study the reduced Poisson action of the quotient of an affine
Poisson group G on the quotient of an affine Poisson-G-variety V. The Poisson morphisms (including equivariant cases) between Poisson affine varieties are also discussed.
Received April 5, 1999, Accepted March 5, 2001 相似文献
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We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be
related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson
and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids. 相似文献
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本文证明了单连通Poisson紧李群切作用及约化Poisson作用于Poisson流形,若带有等动量映射,则可通过调整Poisson流形的Poisson结构,变成保Poisson结构的Poisson作用,并且该作用限制到Poisson流形的辛叶片上,相对于新Poisson结构是Hamiltion作用。我们把Meyer-Marsden-Weinstein约化从Hamiltion作用推广到切Poisson作用,包括正则值和非正则值两种形式。 相似文献
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M. Boucetta 《Differential Geometry and its Applications》2004,20(3):279-291
In a previous paper (C. R. Acad. Sci. Paris Sér. I 333 (2001) 763–768), the author introduced a notion of compatibility between a Poisson structure and a pseudo-Riemannian metric. In this paper, we introduce a new class of Lie algebras called pseudo-Riemannian Lie algebras. The two notions are closely related: we prove that the dual of a Lie algebra endowed with its canonical linear Poisson structure carries a compatible pseudo-Riemannian metric if and only if the Lie algebra is a pseudo-Riemannian Lie algebra. Moreover, the Lie algebra obtained by linearizing at a point a Poisson manifold with a compatible pseudo-Riemannian metric is a pseudo-Riemannian Lie algebra. We also give some properties of the symplectic leaves of such manifolds, and we prove that every Poisson manifold with a compatible Riemannian metric is unimodular. Finally, we study Poisson Lie groups endowed with a compatible pseudo-Riemannian metric, and we give the classification of all pseudo-Riemannian Lie algebras of dimension 2 and 3. 相似文献
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K. Szlachányi 《代数通讯》2013,41(6):2368-2388
Skew monoidal categories are monoidal categories with non-invertible “coherence” morphisms. As shown in a previous article, bialgebroids over a ring R can be characterized as the closed skew monoidal structures on the category Mod-R in which the unit object is RR. This offers a new approach to bialgebroids and Hopf algebroids. Little is known about skew monoidal structures on general categories. In the present article, we study the one-object case: skew monoidal monoids (SMMs). We show that they possess a dual pair of bialgebroids describing the symmetries of the (co)module categories of the SMM. These bialgebroids are submonoids of their own base and are rank 1 free over the base on the source side. We give various equivalent definitions of SMM, study the structure of their (co)module categories, and discuss the possible closed and Hopf structures on a SMM. 相似文献
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K. H. Bhaskara 《Proceedings Mathematical Sciences》1990,100(3):189-202
We establish a one-to-one correspondence between the set of all equivalence classes of affine Poisson structures (defined
on the dual of a finite dimensional Lie algebra) and the set of all equivalence classes of central extensions of the Lie algebra
by ℝ. We characterize all the affine Poisson structures defined on the duals of some lower dimensional Lie algebras. It is
shown that under a certain condition every Poisson structure locally looks like an affine Poisson structure. As an application,
we show the role played by affine Poisson structures in mechanics. Finally, we prove some involution theorems. 相似文献
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Vladimir V. Vershinin 《Acta Appl Math》2003,75(1-3):281-292
Malcev–Poisson structure on a manifold is analogous to a Poisson structure with the Lie identity replaced by a slightly more general Malcev identity. Examples of such structures arise naturally. In the second part of the paper we study Malcev bialgebras. A theorem of characterization is proved. 相似文献