Drinfel’d doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids

DOI10.1090/S1079-6762-98-00050-XzbMath0924.58115MaRDI QIDQ4235487

Kirill Charles Howard Mackenzie

Publication date: 22 March 1999

Published in: Electronic Research Announcements of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/224215

zbMATH Keywords

Poisson manifoldsLie bialgebrasCourant algebroidsDrinfel'd doubleManin triple characterization

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Topological groupoids (including differentiable and Lie groupoids) (22A22) Pseudogroups and differentiable groupoids (58H05)

Related Items (21)

On almost complex Lie algebroids ⋮ Formality theorem for \(\mathfrak{g}\)-manifolds ⋮ Higher vector bundles and multi-graded symplectic manifolds ⋮ Duality functors for triple vector bundles ⋮ Lie algebroid structures on double vector bundles and representation theory of Lie algebroids ⋮ Star products on graded manifolds and α′-corrections to Courant algebroids from string theory ⋮ VB-structures and generalizations ⋮ Atiyah classes and Todd classes of pullback dg Lie algebroids associated with Lie pairs ⋮ Even symplectic supermanifolds and double field theory ⋮ \(Q\)-manifolds and Mackenzie theory ⋮ The Atiyah class of a dg-vector bundle ⋮ Cohomology of skew-holomorphic Lie algebroids ⋮ Pseudo-Dirac structures ⋮ Deformations of linear Lie brackets ⋮ 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 ⋮ Formality and Kontsevich-Duflo type theorems for Lie pairs ⋮ Atiyah classes and Kontsevich–Duflo type theorem for dg manifolds ⋮ Polyvector fields and polydifferential operators associated with Lie pairs ⋮ On a non-Abelian Poincaré lemma ⋮ Double Lie algebroids and second-order geometry. II

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