Extensions of the Poisson bracket to differential forms and multi-vector fields

DOI10.1016/0393-0440(92)90026-WzbMath0748.58008WikidataQ115363127 ScholiaQ115363127MaRDI QIDQ1184422

Antonella Cabras, Alexandre M. Vinogradov

Publication date: 28 June 1992

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

Lie algebraPoisson bracketHamiltonian systemdifferential form

Mathematics Subject Classification ID

Graded Lie (super)algebras (17B70) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Exterior differential systems (Cartan theory) (58A15)

Related Items (24)

Uniqueness and intrinsic properties of non-commutative Koszul brackets ⋮ Eikonal type equations for geometrical singularities of solutions in field theory ⋮ Poisson-Nijenhuis structures and the Vinogradov bracket ⋮ A common generalization of the Frölicher-Nijenhuis bracket and the Schouten bracket for symmetric multivector fields ⋮ Lifting a weak Poisson bracket to the algebra of forms ⋮ The Schouten-Nijenhuis bracket and interior products ⋮ Particle-like structure of Lie algebras ⋮ Gauge invariance and variational trivial problems on the bundle of connections. ⋮ From Poisson algebras to Gerstenhaber algebras ⋮ Alexandre Mikhailovich Vinogradov ⋮ Weyl quantization of degree 2 symplectic graded manifolds ⋮ Variational Poisson-Nijenhuis structures for partial differential equations ⋮ Derived brackets ⋮ A REPORT ON GAUGE INVARIANT FORMS AND VARIATIONAL PROBLEMS ON THE BUNDLE OF CONNECTIONS OF A PRINCIPAL U(1)-BUNDLE AND ON ASSOCIATED VECTOR BUNDLES ⋮ The Bianchi variety ⋮ Gauge-invariant variationally trivial problems on T *M ⋮ A characterization of graded symplectic structures ⋮ Canonical structure of classical field theory in the polymomentum phase space ⋮ The local structure of \(n\)-Poisson and \(n\)-Jacobi manifolds ⋮ POISSON BRACKET IN CLASSICAL FIELD THEORY AS A DERIVED BRACKET ⋮ Z-Graded Extensions of Poisson Brackets ⋮ A note on the existence of graded extensions of Poisson brackets ⋮ Particle-like structure of coaxial Lie algebras ⋮ The standard cohomology of regular Courant algebroids

Cites Work

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• A generalization of Hamiltonian mechanics
• Geometry of nonlinear differential equations
• Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena
• ANALOGUES OF THE OBJECTS OF LIE GROUP THEORY FOR NONLINEAR POISSON BRACKETS

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