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Locally conformal symplectic structures and their generalizations from the point of view of Lie algebras. (English) Zbl 1184.53084

Summary: We study locally conformal symplectic structures and their generalizations from the point of view of transitive Lie algebroids. To consider l.c.s. structures and their generalizations we use Lie algebroids with trivial adjoint Lie algebra bundle \(M\times \mathbb R\) and \(M\times {\mathfrak g}\). We observe that important l.c.s.’s notions can be translated on the Lie algebroid’s language. We generalize l.c.s. structures to \(\mathfrak g\)-l.c.s. structures in which we can consider an arbitrary finite dimensional Lie algebra \(\mathfrak g\) instead of the commutative Lie algebra \(\mathbb R\).

MSC:

53D35 Global theory of symplectic and contact manifolds
22F05 General theory of group and pseudogroup actions
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
58H99 Pseudogroups, differentiable groupoids and general structures on manifolds
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