共查询到20条相似文献,搜索用时 31 毫秒
1.
《Indagationes Mathematicae》2014,25(5):977-991
We introduce the notion of matched pairs of Courant algebroids and give several examples arising naturally from complex manifolds, holomorphic Courant algebroids, and certain regular Courant algebroids. We also consider the matched sum of two Dirac subbundles, one in each of two Courant algebroids forming a matched pair. 相似文献
2.
《Comptes Rendus Mathematique》2008,346(3-4):193-198
We introduce the concept of Loday algebroids, a generalization of Courant algebroids. We define the naive cohomology and modular class of a Loday algebroid, and we show that the modular class of the double of a Lie bialgebroid vanishes. For Courant algebroids, we describe the relation between the naive and standard cohomologies and we conjecture that they are isomorphic when the Courant algebroid is transitive. To cite this article: M. Stiénon, P. Xu, C. R. Acad. Sci. Paris, Ser. I 346 (2008). 相似文献
3.
Mathieu Stiénon 《Comptes Rendus Mathematique》2009,347(9-10):545-550
Hypercomplex structures on Courant algebroids unify holomorphic symplectic structures and usual hypercomplex structures. In this Note, we prove the equivalence of two characterizations of hypercomplex structures on Courant algebroids, one in terms of Nijenhuis concomitants and the other in terms of (almost) torsionfree connections for which each of the three complex structures is parallel. To cite this article: M. Stiénon, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献
4.
Izu Vaisman 《Bulletin of the Brazilian Mathematical Society》2011,42(4):805-830
This is an exposition of the subject, which was developed in the author’s papers [19, 20]. Various results from the theory
of foliations (cohomology, characteristic classes, deformations, etc.) are extended to subalgebroids of Lie algebroids that
generalize the tangent integrable distributions. We also suggest a definition of foliated Courant algebroids and give some
corresponding results and constructions. 相似文献
5.
Henrique Bursztyn 《Advances in Mathematics》2007,211(2):726-765
We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized Kähler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction. The enhanced symmetry group of a Courant algebroid leads us to define extended actions and a generalized notion of moment map. Key examples of generalized Kähler reduced spaces include new explicit bi-Hermitian metrics on CP2. 相似文献
6.
Gaywalee Yamskulna 《代数通讯》2013,41(12):4137-4162
We study relationships between vertex Poisson algebras and Courant algebroids. For any ?-graded vertex Poisson algebra A = ? n∈? A (n), we show that A (1) is a Courant A (0)-algebroid. On the other hand, for any Courant 𝒜-algebroid ?, we construct an ?-graded vertex Poisson algebra A = ? n∈? A (n) such that A (0) is 𝒜 and the Courant 𝒜-algebroid A (1) is isomorphic to ? as a Courant 𝒜-algebroid. 相似文献
7.
Fani Petalidou 《Differential Geometry and its Applications》2005,23(3):282-304
We first recall some basic definitions and facts about Jacobi manifolds, generalized Lie bialgebroids, generalized Courant algebroids and Dirac structures. We establish an one-one correspondence between reducible Dirac structures of the generalized Lie bialgebroid of a Jacobi manifold (M,Λ,E) for which 1 is an admissible function and Jacobi quotient manifolds of M. We study Jacobi reductions from the point of view of Dirac structures theory and we present some examples and applications. 相似文献
8.
Yvette Kosmann-Schwarzbach 《Bulletin of the Brazilian Mathematical Society》2011,42(4):625-649
We study Nijenhuis structures on Courant algebroids in terms of the canonical Poisson bracket on their symplectic realizations.
We prove that the Nijenhuis torsion of a skew-symmetric endomorphism N of a Courant algebroid is skewsymmetric if N
2 is proportional to the identity, and only in this case when the Courant algebroid is irreducible. We derive a necessary and
sufficient condition for a skewsymmetric endomorphism to give rise to a deformed Courant structure. In the case of the double
of a Lie bialgebroid (A, A*), given an endomorphism N of A that defines a skew-symmetric endomorphism N of the double of A, we prove that the torsion ofN is the sum of the torsion of N and that of the transpose of N. 相似文献
9.
Izu Vaisman 《Mediterranean Journal of Mathematics》2010,7(4):415-444
If A is a Lie algebroid over a foliated manifold (M, F){(M, {\mathcal {F}})}, a foliation of A is a Lie subalgebroid B with anchor image TF{T{\mathcal {F}}} and such that A/B is locally equivalent with Lie algebroids over the slice manifolds of F{\mathcal F}. We give several examples and, for foliated Lie algebroids, we discuss the following subjects: the dual Poisson structure
and Vaintrob's supervector field, cohomology and deformations of the foliation, integration to a Lie groupoid. In the last
section, we define a corresponding notion of a foliation of a Courant algebroid A as a bracket–closed, isotropic subbundle B with anchor image TF{T{\mathcal {F}}} and such that B ^ /B{B^{ \bot } /B} is locally equivalent with Courant algebroids over the slice manifolds of F{\mathcal F}. Examples that motivate the definition are given. 相似文献
10.
Ashis Mandal 《代数通讯》2013,41(5):2058-2066
In this note, we will show that exact Courant algebras over a Lie algebra 𝔤 can be characterized via Leibniz 2-cocycles, and the automorphism group of a given exact Courant algebra is in a one-to-one correspondence with first Leibniz cohomology space of 𝔤. 相似文献
11.
Xin ZHANG 《Frontiers of Mathematics in China》2018,13(5):1189-1214
We introduce two Hopf algebroids associated to a proper and holomorphic Lie group action on a complex manifold. We prove that the cyclic cohomology of each Hopf algebroid is equal to the Dolbeault cohomology of invariant differential forms. When the action is cocompact, we develop a generalized complex Hodge theory for the Dolbeault cohomology of invariant differential forms. We prove that every cyclic cohomology class of these two Hopf algebroids can be represented by a generalized harmonic form. This implies that the space of cyclic cohomology of each Hopf algebroid is finite dimensional. As an application of the techniques developed in this paper, we generalize the Serre duality and prove a Kodaira type vanishing theorem. 相似文献
12.
Hillel Gauchman 《Integral Equations and Operator Theory》1983,6(1):31-58
The theory of operator colligations in a Hilbert space is extended to connection colligations on Hilbert bundles. Any invariant subbundle of a Hilbert bundle leads to a decomposition of connection colligation into simpler components. The problem of finding all invariant subbundles of a Hilbert bundle is reduced to a search of subspaces of a fixed Hilbert space which are invariant with respect to the holonomy group of the linear connection. 相似文献
13.
Inverse problem for Lagrangian systems on Lie algebroids and applications to reduction by symmetries
María Barbero-Liñán Marta Farré Puiggalí David Martín de Diego 《Monatshefte für Mathematik》2016,180(4):665-691
The language of Lagrangian submanifolds is used to extend a geometric characterization of the inverse problem of the calculus of variations on tangent bundles to regular Lie algebroids. Since not all closed sections are locally exact on Lie algebroids, the Helmholtz conditions on Lie algebroids are necessary but not sufficient, so they give a weaker definition of the inverse problem. As an application the Helmholtz conditions on Atiyah algebroids are obtained so that the relationship between the inverse problem and the reduced inverse problem by symmetries can be described. Some examples and comparison with previous approaches in the literature are provided. 相似文献
14.
本文研究了Hopf代数胚上的Smash积代数.利用Hopf代数胚的积分理论,获得了Hopf代数胚上的Smash的Maschke型定理并构造了一个Morita关系,推广了Cohen和Fishman在文献[1]中的相应结果.作为应用,获得了Hopf代数胚上的余模代数的Maschke型定理. 相似文献
15.
Let E be a vector bundle of rank 2 over an algebraic curve X of genus g ≥ 2. In this paper, we prove that E is determined by its maximal line subbundles if it is general. By restudying the results of Lange and Narasimhan which relates
the maximal line subbundles with the secant varieties of X, we observe that the proof can be reduced to proving some cohomological conditions satisfied by the maximal line subbundles.
By noting the similarity between these conditions and the notion of very stable bundles, we get the result for the case when
E has Segre invariant s(E) = g. Also by using the elementary transformation, we have the result for the case s(E) = g−1.
I. Choe and J. Choy were supported by KOSEF (R01-2003-000-11634-0) and S. Park was supported by Korea Research Foundation
Grant funded by Korea Government(MOEHRD, Basic Research Promotion Fund) (KRF-2005-070-C00005) 相似文献
16.
In this paper we extend the theory of last multipliers as solutions of the Liouville’s transport equation to Lie algebroids
with their top exterior power as trivial line bundle (previously developed for vector fields and multivectors). We define
the notion of exact section and the Liouville equation on Lie algebroids. The aim of the present work is to develop the theory
of this extension from the tangent bundle algebroid to a general Lie algebroid (e.g. the set of sections with a prescribed
last multiplier is still a Gerstenhaber subalgebra). We present some characterizations of this extension in terms of Witten
and Marsden differentials. 相似文献
17.
18.
A degree 1 non-negative graded super manifold equipped with a degree 1 vector field Q satisfying [Q,Q]=1, namely a so-called NQ-1 manifold is, in plain differential geometry language, a Lie algebroid. We introduce a notion of fibration for such super manifolds, that essentially involves a complete Ehresmann connection. As it is the case for Lie algebras, such fibrations turn out not to be just locally trivial products. We also define homotopy groups and prove the expected long exact sequence associated to a fibration. In particular, Crainic and Fernandes's obstruction to the integrability of Lie algebroids is interpreted as the image of a transgression map in this long exact sequence. 相似文献
19.
Motivated by the work of Crapo and Rota [6] on the lifting of a projective complex, we introduce a class of invariant operations associated to integral-weighted graphs, which we call graphical operations. Such operations generalize the sixth harmonic of a quadranguler set on a projective line. We determine the expansion of the graphical operations in terms of multi-linear bracket polynomials in a Grassmann-Cayley algebra. Reducibility and compositions of such invariant operations are also investigated with a number of examples.Supported by Courant Instructorship, New York University. 相似文献