ON SYMPLECTIC DOUBLE GROUPOIDS AND THE DUALITY OF POISSON GROUPOIDS

DOI10.1142/S0129167X99000185zbMath0961.58008arXivmath/9808005OpenAlexW2039018491MaRDI QIDQ4946812

Kirill Charles Howard Mackenzie

Publication date: 16 May 2001

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9808005

zbMATH Keywords

Poisson groupoidssymplecticdouble Lie groupoidsPoisson vector bundle

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Topological groupoids (including differentiable and Lie groupoids) (22A22) Pseudogroups and differentiable groupoids (58H05)

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Higher vector bundles and multi-graded symplectic manifolds ⋮ Duality functors for triple vector bundles ⋮ Poisson double structures ⋮ Shifted symplectic higher Lie groupoids and classifying spaces ⋮ Poisson groupoids and moduli spaces of flat bundles over surfaces ⋮ From double Lie groupoids to local Lie 2-groupoids ⋮ Vector bundles over Lie groupoids and algebroids ⋮ Double groupoids and the symplectic category ⋮ Double principal bundles ⋮ \(Q\)-manifolds and Mackenzie theory ⋮ The infinitesimal counterpart of tangent presymplectic groupoids of higher order ⋮ Double Lie algebroids and representations up to homotopy ⋮ The geometrization of \(\mathbb{N}\)-manifolds of degree 2 ⋮ The structure of double groupoids ⋮ Pseudo-Dirac structures ⋮ 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 ⋮ Double Lie algebroids and second-order geometry. II ⋮ Quasi-bialgebras and dynamical \(r\)-matrices ⋮ Drinfel’d doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids

Cites Work

• Algebraic constructions in the category of Lie algebroids
• Coisotropic calculus and Poisson groupoids
• Determination of a double Lie groupoid by its core diagram
• Double Lie algebroids and second-order geometry. I
• Lie bialgebroids and Poisson groupoids
• Exact Gerstenhaber algebras and Lie bialgebroids
• ON POISSON GROUPOIDS
• Dirac Manifolds

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