Double Lie algebroids and second-order geometry. II

DOI10.1006/aima.1999.1892zbMath0971.58015OpenAlexW4212795658MaRDI QIDQ1584526

Kirill Charles Howard Mackenzie

Publication date: 28 October 2001

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.1999.1892

zbMATH Keywords

Lie groupoidLie bialgebroidLie algebroidLie bialgebraPoisson Lie groupPoisson groupoiddouble Lie groupoidaffinoiddouble Lie algebroiddouble tangent bundlestar sectionsymplectic and Poisson geometry

Mathematics Subject Classification ID

Topological groupoids (including differentiable and Lie groupoids) (22A22) Pseudogroups and differentiable groupoids (58H05)

Related Items (61)

Tensor categories attached to double groupoids. ⋮ Homogeneous spaces of Dirac groupoids ⋮ Higher vector bundles and multi-graded symplectic manifolds ⋮ Linearization of Poisson groupoids ⋮ Lie algebroid structures on double vector bundles and representation theory of Lie algebroids ⋮ Killing sections and sigma models with Lie algebroid targets ⋮ Poisson double structures ⋮ Discrete Lagrangian field theories on Lie groupoids ⋮ Lie algebroids, Lie groupoids and TFT ⋮ Vertical symmetries of Cartan geometries ⋮ The Schouten-Nijenhuis bracket and interior products ⋮ Hom-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids ⋮ Strong topologies for spaces of smooth maps with infinite-dimensional target ⋮ VB-structures and generalizations ⋮ \(L_{\infty}\)-algebra actions ⋮ Pre-Courant algebroids ⋮ Some exotic characteristic homomorphism for Lie algebroids ⋮ Gauging without initial symmetry ⋮ Lie algebroid fibrations ⋮ Categorification of \(\mathsf{VB}\)-Lie algebroids and \(\mathsf{VB}\)-Courant algebroids ⋮ Towards a 2-dimensional notion of holonomy. ⋮ Reduction of symplectic groupoids and quotients of quasi-Poisson manifolds ⋮ Vector bundles over Lie groupoids and algebroids ⋮ Local symmetries in gauge theories in a finite-dimensional setting ⋮ n-Tuple principal bundles ⋮ Duality for Hopf algebroids ⋮ Representations of orbifold groupoids ⋮ The geometry of graded cotangent bundles ⋮ Representation up to homotopy of hom-Lie algebroids ⋮ Infinitesimal Automorphisms of VB-Groupoids and Algebroids ⋮ On cosymplectic groupoids ⋮ Even symplectic supermanifolds and double field theory ⋮ Double principal bundles ⋮ Representation and central extension of hom-Lie algebroids ⋮ Duality for graded manifolds ⋮ On the geometry of prequantization spaces ⋮ Determination of a double Lie groupoid by its core diagram ⋮ On the integration of Poisson homogeneous spaces ⋮ \(Q\)-manifolds and Mackenzie theory ⋮ The holonomy groupoid of a locally topological groupoid ⋮ Double groupoids and homotopy 2-types ⋮ Tulczyjew triples and higher Poisson/Schouten structures on Lie algebroids ⋮ Characteristic classes of Lie algebroid morphisms ⋮ Group-groupoids and monodromy groupoids ⋮ On the role of effective representations of Lie groupoids ⋮ Double Lie algebroids and representations up to homotopy ⋮ Linear duals of graded bundles and higher analogues of (Lie) algebroids ⋮ The structure of double groupoids ⋮ Foliated groupoids and infinitesimal ideal systems ⋮ Holomorphic Jacobi manifolds and holomorphic contact groupoids ⋮ Ehresmann doubles and Drinfel'd doubles for Lie algebroids and Lie bialgebroids ⋮ Preface to special issue in memory of Kirill C. H. Mackenzie (1951--2020). I ⋮ Transitive double Lie algebroids via core diagrams ⋮ Atiyah classes and Kontsevich–Duflo type theorem for dg manifolds ⋮ On the Lie 2-algebra of sections of an \(\mathcal{LA}\)-groupoid ⋮ Lie groupoids and Lie algebroids in physics and noncommutative geometry ⋮ Holonomy and parallel transport for abelian gerbes ⋮ \(\mathcal{VB}\)-algebroid morphisms and representations up to homotopy ⋮ Star calculus on Jacobi manifolds. ⋮ Representation up to homotopy of double algebroids and their transgression classes ⋮ Representation up to Homotopy and Hom-Lie Algebroid Modules

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Poisson homogeneous spaces and Lie algebroids associated to Poisson actions
• Algebraic constructions in the category of Lie algebroids
• Coisotropic calculus and Poisson groupoids
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations
• Determination of a double Lie groupoid by its core diagram
• Double Lie algebroids and second-order geometry. I
• Lie bialgebroids and Poisson groupoids
• Manin triples for Lie bialgebroids
• Tangent and cotangent lifts and graded Lie algebras associated with Lie algebroids
• On Poisson homogeneous spaces of Poisson-Lie groups
• Tangent Dirac structures
• Drinfel’d doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids
• Matched pairs of Lie algebroids
• Classical lifting processes and multiplicative vector fields
• Lie Algebroids and Lie Pseudoalgebras
• ON SYMPLECTIC DOUBLE GROUPOIDS AND THE DUALITY OF POISSON GROUPOIDS
• AFFINE POISSON STRUCTURES

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