Manin triples for Lie bialgebroids
From MaRDI portal
Publication:1366612
DOI10.4310/jdg/1214459842zbMath0885.58030arXivdg-ga/9508013OpenAlexW1538654631WikidataQ115175739 ScholiaQ115175739MaRDI QIDQ1366612
Ping Xu, Alan Weinstein, Zhang-Ju Liu
Publication date: 15 September 1997
Published in: Journal of Differential Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/dg-ga/9508013
Lie algebras of vector fields and related (super) algebras (17B66) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Global differential geometry (53C99) Topological groupoids (including differentiable and Lie groupoids) (22A22) Pseudogroups and differentiable groupoids (58H05)
Related Items
A note on multi-oriented graph complexes and deformation quantization of Lie bialgebroids, Dissections and automorphisms of regular Courant algebroids, Simultaneous deformations and Poisson geometry, Lectures on Cohomology, T-Duality, and Generalized Geometry, Metastring theory and modular space-time, Sigma models for genuinely non-geometric backgrounds, 2-PLECTIC MANIFOLDS AND ITS RELATION WITH COURANT ALGEBROIDS, Star products on graded manifolds and α′-corrections to Courant algebroids from string theory, Higher multi-Courant algebroids, Deformations and cohomologies of relative Rota-Baxter operators on Lie algebroids and Koszul-Vinberg structures, Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids, Exact Lie bialgebroids and Poisson groupoids, Modular classes revisited, Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures, Courant cohomology, Cartan calculus, connections, curvature, characteristic classes, Canonical functions, differential graded symplectic pairs in supergeometry, and Alexandrov-Kontsevich-Schwartz-Zaboronsky sigma models with boundaries, Dirac geometry of the holonomy fibration, Contact Courant algebroids and \(L_\infty\)-algebras, Strings in singular space-times and their universal gauge theory, Hom-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids, Generalized almost product structures and generalized CRF-structures, The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics, Ricci flow, Courant algebroids, and renormalization of Poisson-Lie T-duality, Shifted derived Poisson manifolds associated with Lie pairs, Double field theory and membrane sigma-models, Poisson-generalized geometry and R-flux, Deformations of symplectic foliations, Integration of Lie 2-algebras and their morphisms, Compatible \(L_\infty \)-algebras, THREE-DIMENSIONAL TOPOLOGICAL FIELD THEORY INDUCED FROM GENERALIZED COMPLEX STRUCTURE, Reviving 3D $ \mathcal{N}=8$ superconformal field theories, Pre-Courant algebroids, Algebraic structure of holomorphic Poisson cohomology on nilmanifolds, Group actions on DG-manifolds and exact Courant algebroids, Super AKSZ construction, integral forms, and the 2-dimensional \(\mathcal{N} = (1, 1)\) sigma model, Generalized CRF-structures, Nonabelian omni-Lie algebroids, Modules and representations up to homotopy of Lie \(n\)-algebroids, `Anti-commutable' local pre-Leibniz algebroids and admissible connections, Poisson quasi-Nijenhuis deformations of the canonical PN structure, The universal Lie \(\infty\)-algebroid of a singular foliation, Higher extensions of Lie algebroids, Odd transgression for Courant algebroids, Twisted Courant algebroids and coisotropic Cartan geometries, Courant brackets on noncommutative algebras and omni-Lie algebras, Higher algebra over the Leibniz operad, Generalized deformation of complex structures on nilmanifolds, DIRAC STRUCTURES FROM LIE INTEGRABILITY, Bianchi identities for non‐geometric fluxes from quasi‐Poisson structures to Courant algebroids, Topological field theories induced by twisted \(R \)-Poisson structure in any dimension, Weyl quantization of degree 2 symplectic graded manifolds, Momentum section on Courant algebroid and constrained Hamiltonian mechanics, Some properties of Dirac-Nijenhuis manifolds, Courant algebroids, Poisson-Lie T-duality, and Type II supergravities, Algebroid structures on para-Hermitian manifolds, Modular classes of Loday algebroids, Reduction of generalized complex structures, Poisson-Lie T-duality of WZW model via current algebra deformation, Nijenhuis forms on \(L_\infty\)-algebras and Poisson geometry, Poisson quasi-Nijenhuis manifolds and the Toda system, On LA-Courant algebroids and Poisson Lie 2-algebroids, A unique connection for Born geometry, Background independent action for double field theory, Rozansky-Witten-type invariants from symplectic Lie pairs, Foliation-coupling Dirac structures, Generalized Moser lemma, Dirac submanifolds and Poisson involutions, Derived brackets for fat Leibniz algebras, Courant bracket as T-dual invariant extension of Lie bracket, Leibniz algebras with derivations, Higher nonabelian omni-Lie algebroids, Twisted chiral de Rham complex, generalized geometry, and T-duality, On curvature and torsion in Courant algebroids, Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids, Extended manifolds and extended equivariant cohomology, Abelian complex structures and generalizations, Gravity theory on Poisson manifold with R -flux, More on doubled aspects of algebroids in double field theory, Lie 2-algebroids and matched pairs of 2-representations: a geometric approach, Linearization of the higher analogue of Courant algebroids, Integrability of quotients in Poisson and Dirac geometry, Hitchhiker's guide to Courant algebroid relations, Algebroids, AKSZ constructions and doubled geometry, Preface to special issue in memory of Kirill C. H. Mackenzie (1951--2020). I, Brackets by any other name, Fluxes in exceptional field theory and threebrane sigma-models, On the twisted Dorfman-Courant like brackets, On Lie bialgebroid crossed modules, Double field theory algebroid and curved L ∞-algebras, The deformation \(L_\infty\) algebra of a Dirac-Jacobi structure, The natural operators similar to the twisted Courant bracket one, THE GAUGING OF TWO-DIMENSIONAL BOSONIC SIGMA MODELS ON WORLD-SHEETS WITH DEFECTS, Brane current algebras and generalised geometry from QP manifolds. Or, ``when they go high, we go low, Graded generalized geometry, Momentum sections in Hamiltonian mechanics and sigma models, Dimensional reduction of Courant sigma models and Lie theory of Poisson groupoids, Complex Dirac structures: invariants and local structure, Reduction of Jacobi manifolds via Dirac structures theory, The standard cohomology of regular Courant algebroids, Drinfel’d doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids, Dirac-Nijenhuis structures on Lie bialgebroids, Almost homogeneous Poisson manifolds, From Leibniz algebras to Lie 2-algebras, Ricci tensor in graded geometry, \(O(d, d)\)-duality in string theory, The modular class of a Dirac map, Homogeneous spaces of Dirac groupoids, The Pontryagin class for pre-Courant algebroids, Integration of twisted Dirac brackets, Pseudo-Poisson Nijenhuis manifolds, BV quantization of topological open membranes, Higher vector bundles and multi-graded symplectic manifolds, On higher dimensional exact Courant algebroids, Poisson-Lie T-duality of string effective actions: a new approach to the dilaton puzzle, Constant symplectic 2-groupoids, Left-symmetric bialgebroids and their corresponding Manin triples, Deformations of Courant algebroids and Dirac structures via blended structures, Courant-Dorfman algebras and their cohomology., Topological membranes, current algebras and H-flux-R-flux duality based on Courant algebroids, Poisson-Lie T-duality as a boundary phenomenon of Chern-Simons theory, Higher gauge theories from Lie \(n\)-algebras and off-shell covariantization, Chern-Weil homomorphism in twisted equivariant cohomology, \(C^\ast\)-algebras of 2-groupoids, Dorfman connections and Courant algebroids, Monge-Ampère equations and generalized complex geometry -- the two-dimensional case, Formal deformations of Dirac structures, On higher-dimensional Courant algebroids, The Schouten-Nijenhuis bracket and interior products, Characteristic classes of gauge systems, The first Pontryagin class of a quadratic Lie 2-algebroid, Reduction of Courant algebroids and generalized complex structures, Poisson geometry, Symmetries in generalized Kähler geometry, Poisson quasi-Nijenhuis manifolds, Graded contact manifolds and contact Courant algebroids, \(B_n\)-generalized geometry and \(G_2^2\)-structures, Deformation of Dirac structures along isotropic subbundles, Jacobi quasi-Nijenhuis algebroids, A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds, Generalized Kähler geometry, Foliated Lie and Courant algebroids, Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds, Leibniz algebroids, twistings and exceptional generalized geometry, Holomorphic Poisson structure and its cohomology on nilmanifolds, Generalized complex structures and Lie brackets, Nijenhuis structures on Courant algebroids, From double Lie groupoids to local Lie 2-groupoids, Lie and Courant algebroids on foliated manifolds, Dirac actions and Lu's Lie algebroid, Omni-Lie 2-algebras and their Dirac structures, Poisson-Lie T-duality and Courant algebroids, Transverse geometry and generalized complex structures, \(L _{\infty }\)-algebras from multisymplectic geometry, Invariant frames for vector bundles and applications, Generalised kinematics for double field theory, Dirac structures, nonholonomic systems and reduction, Generalized complex geometry, Nambu structures and associated bialgebroids, Torsion-free generalized connections and heterotic supergravity, Lagrangian approach to sheaves of vertex algebras, Dirac-Nijenhuis manifolds, Holomorphic Poisson cohomology, From hypercomplex to holomorphic symplectic structures, Even symplectic supermanifolds and double field theory, Symplectic structures on the integration of exact Courant algebroids, Poisson geometry from a Dirac perspective, Deformations of pre-symplectic structures: a Dirac geometry approach, On deformations of generalized Calabi-Yau and generalized \(\mathrm{SU}(n)\)-structures, Double Bruhat cells and symplectic groupoids, \(Q\)-manifolds and Mackenzie theory, Quasiclassical Lian-Zuckerman homotopy algebras, Courant algebroids and gauge theory, Omni-Lie algebroids, On higher analogues of Courant algebroids, Derived brackets, On Jacobi quasi-Nijenhuis algebroids and Courant-Jacobi algebroid morphisms, Contact manifolds and generalized complex structures, Geometry of Maurer-Cartan elements on complex manifolds, Doubling, T-duality and generalized geometry: a simple model, Lie bialgebroids of generalized CRF-manifolds, Reduction and submanifolds of generalized complex manifolds, Courant algebroids, Poisson sigma model on the sphere, Membrane sigma-models and quantization of non-geometric flux backgrounds, D-branes in generalized geometry and Dirac-Born-Infeld action, Tangent of a Courant algebroid, Poisson-Nijenhuis structures on oriented 3D-manifolds, Poisson structures and generalized Kähler submanifolds, Goto's generalized Kähler stability theorem, Matched pairs of Courant algebroids, Pseudo-Dirac structures, Variation of Hodge structure for generalized complex manifolds, Hypercomplex structures on Courant algebroids, Local structure of generalized contact manifolds, Poisson quasi-Nijenhuis structures with background, Split Courant algebroids as \(L_\infty\)-structures, Generalized complex structures on Kodaira surfaces, On the geometric structure of Hamiltonian systems with ports, Double Lie algebroids and second-order geometry. II, Free Courant and derived Leibniz pseudoalgebras, Dirac sigma models, On the geometric interpretation of certain vertex algebras and their modules, GROUPOIDS, LOOP SPACES AND QUANTIZATION OF 2-PLECTIC MANIFOLDS, Current algebras, generalised fluxes and non-geometry, POISSON GEOMETRY IN CONSTRAINED SYSTEMS, The natural operators similar to the twisted courant bracket on couples of vector fields and p-forms, Hom-Poisson-Nijenhuis structures and Hom-Dirac structures, Noncommutative Poisson vertex algebras and Courant-Dorfman algebras, G‐Algebroids: A Unified Framework for Exceptional and Generalised Geometry, and Poisson–Lie Duality, Courant Sigma Model and ‐algebras, Exceptional Algebroids and Type IIB Superstrings, Exceptional Algebroids and Type IIA Superstrings, Twisted C‐Brackets, Stability of fixed points of Dirac structures, \(B_n\)-generalized pseudo-Kähler structures, Metric algebroid and Poisson-Lie T-duality in DFT, Poisson groupoids and moduli spaces of flat bundles over surfaces, Omni-Representations of Leibniz Algebras, Courant-Nijenhuis algebroids, Categorification of \(\mathsf{VB}\)-Lie algebroids and \(\mathsf{VB}\)-Courant algebroids, A QP perspective on topology change in Poisson–Lie T-duality, The Atiyah class of generalized holomorphic vector bundles, Double field theory, twistors, and integrability in 4-manifolds, Doubled aspects of algebroids and gauge symmetry in double field theory, Metric-Bourbaki algebroids: Cartan calculus for M-theory, Courant-Dorfman algebras of differential operators and Dorfman connections of Courant algebroids, Cohomology of hemistrict Lie 2-algebras, Generalized almost para-contact manifolds, Omni n-Lie algebras and linearization of higher analogues of Courant algebroids, Unnamed Item, Six-dimensional (1,0) superconformal models and higher gauge theory, Towards a double field theory on para-Hermitian manifolds, Dirac structures and dynamical \(r\)-matrices, Unnamed Item, General Yang–Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical frameworkorFrom Bianchi identities to twisted Courant algebroids, Homotopy Loday Algebras and Symplectic $2$-Manifolds, Deformation spaces and normal forms around transversals, Doubled aspects of Vaisman algebroid and gauge symmetry in double field theory, On the gauge-natural operators similar to the twisted Dorfman-Courant bracket, Topological T-duality for torus bundles with monodromy, Global aspects of doubled geometry and pre-rackoid, Born sigma-models for para-Hermitian manifolds and generalized T-duality
