scholarly journals Constructions of Generalized Complex Structures in Dimension Four

2012 ◽  
Vol 314 (2) ◽  
pp. 351-371 ◽  
Author(s):  
Rafael Torres
Keyword(s):  
Complex Structures ◽  
Generalized Complex Structures ◽  
Generalized Complex

scholarly journals On cohomological decomposition of generalized-complex structures

2015 ◽  
Vol 98 ◽  
pp. 227-241 ◽  
Author(s):  
Daniele Angella ◽  
Simone Calamai ◽  
Adela Latorre
Keyword(s):  
Complex Structures ◽  
Generalized Complex Structures ◽  
Generalized Complex

scholarly journals Stable generalized complex structures

2017 ◽  
Vol 116 (5) ◽  
pp. 1075-1111 ◽  
Author(s):  
Gil R. Cavalcanti ◽  
Marco Gualtieri
Keyword(s):  
Complex Structures ◽  
Generalized Complex Structures ◽  
Generalized Complex

scholarly journals VB-Courant Algebroids, E-Courant Algebroids and Generalized Geometry

2018 ◽  
Vol 61 (3) ◽  
pp. 588-607 ◽  
Author(s):  
Honglei Lang ◽  
Yunhe Sheng ◽  
Aïssa Wade
Keyword(s):  
Lie Algebra ◽  
Complex Structure ◽  
Contact Structures ◽  
Complex Structures ◽  
Courant Algebroids ◽  
Courant Algebroid ◽  
Generalized Complex Structures ◽  
Generalized Complex Structure ◽  
Generalized Geometry ◽  
Generalized Complex

AbstractIn this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids, and we construct some examples of E-Courant algebroids. Then we introduce the notion of a generalized complex structure on an E-Courant algebroid, unifying the usual generalized complex structures on even-dimensional manifolds and generalized contact structures on odd-dimensional manifolds. Moreover, we study generalized complex structures on an omni-Lie algebroid in detail. In particular, we show that generalized complex structures on an omni-Lie algebra gl(V) ⊕ V correspond to complex Lie algebra structures on V.

scholarly journals TOPOLOGICAL STRINGS ON NONCOMMUTATIVE MANIFOLDS

2004 ◽  
Vol 01 (01n02) ◽  
pp. 49-81 ◽  
Author(s):  
ANTON KAPUSTIN
Keyword(s):  
Sigma Models ◽  
Path Integral ◽  
Sigma Model ◽  
Chern Character ◽  
Complex Structures ◽  
Holomorphic Maps ◽  
Generalized Complex Structures ◽  
Noncommutative Manifolds ◽  
Special Cases ◽  
Generalized Complex

We identify a deformation of the N=2 supersymmetric sigma model on a Calabi–Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkähler X such deformations allow one to interpolate continuously between the A-model and the B-model. For generic values of the noncommutativity and the B-field, properties of the topologically twisted sigma-models can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigma-model is localized on generalized holomorphic maps, whereas for the A-model and the B-model it is localized on holomorphic and constant maps, respectively. The geometry of topological D-branes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological D-branes, which includes A-branes and B-branes as special cases.

scholarly journals Some remarks on invariant Poisson quasi-Nijenhuis structures on Lie groups

2019 ◽  
Vol 16 (07) ◽  
pp. 1950097
Author(s):  
Ghorbanali Haghighatdoost ◽  
Zohreh Ravanpak ◽  
Adel Rezaei-Aghdam
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Lie Group ◽  
Baxter Equation ◽  
Complex Structures ◽  
Lie Bialgebra ◽  
Text Structures ◽  
Generalized Complex Structures ◽  
Generalized Complex

We study right-invariant (respectively, left-invariant) Poisson quasi-Nijenhuis structures on a Lie group [Formula: see text] and introduce their infinitesimal counterpart, the so-called r-qn structures on the corresponding Lie algebra [Formula: see text]. We investigate the procedure of the classification of such structures on the Lie algebras and then for clarity of our results we classify, up to a natural equivalence, all [Formula: see text]-[Formula: see text] structures on two types of four-dimensional real Lie algebras. We mention some remarks on the relation between [Formula: see text]-[Formula: see text] structures and the generalized complex structures on the Lie algebras [Formula: see text] and also the solutions of modified Yang–Baxter equation (MYBE) on the double of Lie bialgebra [Formula: see text]. The results are applied to some relevant examples.

scholarly journals Splitting theorems for Poisson and related structures

2019 ◽  
Vol 2019 (754) ◽  
pp. 281-312 ◽  
Author(s):  
Henrique Bursztyn ◽  
Hudson Lima ◽  
Eckhard Meinrenken
Keyword(s):  
Symplectic Manifold ◽  
Poisson Structure ◽  
Poisson Manifold ◽  
Lie Algebroids ◽  
Complex Structures ◽  
Splitting Theorem ◽  
Dirac Structures ◽  
Novel Approach ◽  
Generalized Complex Structures ◽  
Generalized Complex

Abstract According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results are known, e.g., for Lie algebroids, Dirac structures and generalized complex structures. In this paper, we develop a novel approach towards these results that leads to various generalizations, including their equivariant versions as well as their formulations in new contexts.

scholarly journals AV-Courant Algebroids and Generalized CR Structures

2011 ◽  
Vol 63 (4) ◽  
pp. 938-960 ◽  
Author(s):  
David Li-Bland
Keyword(s):  
Contact Structure ◽  
Complex Structures ◽  
Lie Algebroid ◽  
Courant Algebroids ◽  
The Third ◽  
Cr Structure ◽  
Generalized Complex Structures ◽  
Generalized Complex ◽  
Cr Structures

Abstract We construct a generalization of Courant algebroids that are classified by the third coho- mology group H3(A , V), where A is a Lie Algebroid, and V is an A-module. We see that both Courant algebroids and structures are examples of them. Finally we introduce generalized CR structures on a manifold, which are a generalization of generalized complex structures, and show that every CR structure and contact structure is an example of a generalized CR structure.

scholarly journals Reduction of Courant algebroids and generalized complex structures

2007 ◽  
Vol 211 (2) ◽  
pp. 726-765 ◽  
Author(s):  
Henrique Bursztyn ◽  
Gil R. Cavalcanti ◽  
Marco Gualtieri
Keyword(s):  
Complex Structures ◽  
Courant Algebroids ◽  
Generalized Complex Structures ◽  
Generalized Complex
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