共查询到20条相似文献,搜索用时 15 毫秒
1.
Henrique Bursztyn Thiago Drummond 《Bulletin of the Brazilian Mathematical Society》2013,44(4):709-730
The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frölicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued forms on Lie groupoids and show that they naturally form a graded Lie subalgebra. Along the way, we discuss various examples and different characterizations of multiplicative vector-valued forms. 相似文献
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Jure Kališnik 《Czechoslovak Mathematical Journal》2011,61(3):653-672
The classical Serre-Swan’s theorem defines an equivalence between the category of vector bundles and the category of finitely
generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend
these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category
of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially
defined on the Morita category of étale Lie groupoids and we show that the given correspondence represents a natural equivalence
between them. 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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David A. Towers 《代数通讯》2017,45(3):1284-1293
The purpose of this paper is to continue the study of chief factors of a Lie algebra and to prove a further strengthening of the Jordan–Hölder theorem for chief series. 相似文献
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Lina Ji 《Journal of Mathematical Analysis and Applications》2012,389(2):979-988
The functionally generalized separable solutions of the generalized porous medium equations with power law and exponential diffusivity are studied by using the conditional Lie–Bäcklund symmetry method. The variant forms of the considered equations, which admit the linear conditional Lie–Bäcklund symmetries, are identified. A number of examples are considered and some exact solutions, defined on the polynomial, trigonometric and exponential invariant subspaces determined by the linear conditional Lie–Bäcklund symmetries, are constructed. 相似文献
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Lie bialgebras of generalized Witt type 总被引:11,自引:0,他引:11
SONG Guang''''ai & SU Yucai College of Mathematics Information Science Shandong Institute of Business Technology Yantai China Department of Mathematics University of Science Technology of China Hefei China Department of Mathematics Shanghai Jiaotong University Shanghai China 《中国科学A辑(英文版)》2006,49(4):533-544
In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial. 相似文献
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We study the external and internal Zappa–Szép product of topological groupoids. We show that under natural continuity assumptions the Zappa–Szép product groupoid is étale if and only if the individual groupoids are étale. In our main result we show that the \(C^*\)-algebra of a locally compact Hausdorff étale Zappa–Szép product groupoid is a \(C^*\)-blend, in the sense of Exel, of the individual groupoid \(C^*\)-algebras. We finish with some examples, including groupoids built from \(*\)-commuting endomorphisms, and skew product groupoids. 相似文献
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In this paper we analyze the matrix differential system X' = [N,X2], where N is skew-symmetric and X(0) is symmetric. We prove that it is isospectral and that it is endowed with a Poisson
structure, and we discuss its invariants and Casimirs. Formulation of the Poisson problem in a Lie-Poisson setting, as a flow
on a dual of a Lie algebra, requires a computation of its faithful representation. Although the existence of a faithful representation,
assured by the Ado theorem and a symbolic algorithm, due to de Graaf, exists for the general computation of faithful representations
of Lie algebras, the practical problem of forming a "tight" representation, convenient for subsequent analytic and numerical
work, belongs to numerical algebra. We solve it for the Poisson structure corresponding to the equation X' = [N,X2]. 相似文献
12.
A. N. Sergeev 《Journal of Mathematical Sciences》2018,235(6):756-787
We review recent results obtained at the intersection of the theory of quantum deformed Calogero–Moser–Sutherland systems and the theory of Lie superalgebras. We begin with a definition of admissible deformations of root systems of basic classical Lie superalgebras. For classical series, we prove the existence of Lax pairs. Connections between infinite-dimensional Calogero–Moser–Sutherland systems, deformed quantum CMS systems, and representation theory of Lie superalgebras are discussed. 相似文献
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Amirzadeh-Fard H. Haghighatdoost G. Kheradmandynia P. Rezaei-Aghdam A. 《Theoretical and Mathematical Physics》2020,205(2):1393-1410
Theoretical and Mathematical Physics - Using the adjoint representations of Lie algebras, we classify all Jacobi structures on real two- and three-dimensional Lie groups. We also study... 相似文献
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We consider the Lu–Weinstein–Soibelman Drinfeld double D and a pair of -models associated with it. We show that the Poisson–Lie T-duality relating them can be extended to include string configurations with a nonunit non-Abelian momentum. The dual string configuration (living on the maximal compact subgroup of D) then develops a nontrivial monodromy taking values in the Weyl alcove. We also give the duality-invariant action of this dynamical system and describe the analogous phenomenon for the dressing cosets. 相似文献
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The equations defining both the exact and the computed solution to an initial value problem are related to a single functional equation, which can be regarded as prototypical. The functional equation can be solved in terms of a formal Taylor series, which can also be generated using an iteration process. This leads to the formal Taylor expansions of the solution and approximate solutions to initial value problems. The usual formulation, using rooted trees, can be modified to allow for linear combinations of trees, and this gives an insight into the nature of order conditions for explicit Runge–Kutta methods. A short derivation of the family of fourth order methods with four stages is given. 相似文献
20.
Chun-Gil Park 《Bulletin of the Brazilian Mathematical Society》2005,36(3):333-362
Let X and Y be vector spaces. It is shown that a mapping f : X → Y satisfies the functional equation
if and only if the mapping f : X → Y is additive, and prove the Cauchy–Rassias stability of the functional equation (‡) in Banach modules over a unital C*-algebra. Let
and
be unital C*-algebras, Poisson C*-algebras, Poisson JC*-algebras or Lie JC*-algebras. As an application, we show that every almost homomorphism h :
→
of
into
is a homomorphism when h((d + 2)nuy) = h((d + 2)nu)h(y) or h((d + 2)nu ∘ y) = h((d + 2)nu) ∘ h(y) for all unitaries u ∈
, all y ∈
, and n = 0, 1, 2, • • • .
Moreover, we prove the Cauchy–Rassias stability of homomorphisms in C*-algebras, Poisson C*-algebras, Poisson JC*-algebras or Lie JC*-algebras.
Supported by Korea Research Foundation Grant KRF-2004-041-C00023. 相似文献
(‡) |