International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 09/2013, Volume 10, Issue 8

We review origins and main properties of the most important bracket operations appearing canonically in differential geometry and mathematical physics in the classical, as well as in the supergeometric setting...

Nijenhuis tensor | Poisson bracket | Lie bracket | Courant bracket | Lie algebroid | HAMILTONIAN-FORMALISM | CALCULUS | NIJENHUIS | PHYSICS, MATHEMATICAL | MECHANICS | NAMBU-POISSON | COHOMOLOGY | ISOMORPHISMS | LIE ALGEBROIDS | DIRAC STRUCTURES | DYNAMICS | Mathematics - Differential Geometry

Nijenhuis tensor | Poisson bracket | Lie bracket | Courant bracket | Lie algebroid | HAMILTONIAN-FORMALISM | CALCULUS | NIJENHUIS | PHYSICS, MATHEMATICAL | MECHANICS | NAMBU-POISSON | COHOMOLOGY | ISOMORPHISMS | LIE ALGEBROIDS | DIRAC STRUCTURES | DYNAMICS | Mathematics - Differential Geometry

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 11/2018, Volume 15, Issue 11

We propose an extension of n-ary Nambu-Poisson bracket to superspace R-n vertical bar m and construct by means of superdeterminant a family of Nambu-Poisson algebras of even degree functions...

Nambu-Poisson bracket | Hamiltonian mechanics | Poisson bracket | Nambu mechanics | supermanifold | Filippov-Jacobi identity | PHYSICS, MATHEMATICAL

Nambu-Poisson bracket | Hamiltonian mechanics | Poisson bracket | Nambu mechanics | supermanifold | Filippov-Jacobi identity | PHYSICS, MATHEMATICAL

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 10/2018, Volume 132, pp. 358 - 362

We give a method to construct Poisson brackets {⋅,⋅} on Banach manifolds M, for which the value of {f,g...

Banach manifolds | Operational vector fields | Queer Poisson brackets | Higher order derivations | MATHEMATICS | PHYSICS, MATHEMATICAL

Banach manifolds | Operational vector fields | Queer Poisson brackets | Higher order derivations | MATHEMATICS | PHYSICS, MATHEMATICAL

Journal Article

Letters in Mathematical Physics, ISSN 1573-0530, 2004, Volume 69, Issue 1, pp. 61 - 87

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties...

Odd Poisson supermanifold | Courant algebroid | Vinogradov bracket | derived bracket | Courant bracket | Mathematical and Computational Physics | Poisson structure with background | Physics | Geometry | Loday–Leibniz algebra | Lie algebroid | Group Theory and Generalizations | Statistical Physics | FIELDS | Loday-Leibniz algebra | LIE BIALGEBROIDS | PHYSICS, MATHEMATICAL | odd Poisson supermanifold | FORMS | Derived bracket | ALGEBRAS | COHOMOLOGY | DIRAC STRUCTURES | POISSON MANIFOLDS | OPERATORS | GEOMETRY

Odd Poisson supermanifold | Courant algebroid | Vinogradov bracket | derived bracket | Courant bracket | Mathematical and Computational Physics | Poisson structure with background | Physics | Geometry | Loday–Leibniz algebra | Lie algebroid | Group Theory and Generalizations | Statistical Physics | FIELDS | Loday-Leibniz algebra | LIE BIALGEBROIDS | PHYSICS, MATHEMATICAL | odd Poisson supermanifold | FORMS | Derived bracket | ALGEBRAS | COHOMOLOGY | DIRAC STRUCTURES | POISSON MANIFOLDS | OPERATORS | GEOMETRY

Journal Article

Journal of Algebra, ISSN 0021-8693, 12/2017, Volume 492, pp. 212 - 233

We propose a non-skew-symmetric generalization of the original definition of double Poisson Bracket by M. Van den Bergh...

Noncommutative geometry | Integrable systems | Poisson brackets | Representation algebras | MATHEMATICS | ALGEBRAS | Mathematics - Quantum Algebra

Noncommutative geometry | Integrable systems | Poisson brackets | Representation algebras | MATHEMATICS | ALGEBRAS | Mathematics - Quantum Algebra

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 12/2017, Volume 115, Issue 6, pp. 1149 - 1169

We apply new techniques to compute Gerstenhaber brackets on the Hochschild cohomology of a skew group algebra formed from a polynomial ring and a finite group (in characteristic 0...

16E40 | 16S35 (primary) | MATHEMATICS | POISSON MANIFOLDS | ALGEBRAS | HOCHSCHILD COHOMOLOGY | PRODUCTS | DEFORMATIONS

16E40 | 16S35 (primary) | MATHEMATICS | POISSON MANIFOLDS | ALGEBRAS | HOCHSCHILD COHOMOLOGY | PRODUCTS | DEFORMATIONS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 04/2017, Volume 114, pp. 404 - 419

We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin–Novikov type with D independent variables...

Deformations of Poisson structures | Poisson cohomology | Poisson brackets of hydrodynamic type | Mathematical Physics | Physics and Astronomy(all) | Geometry and Topology | MATHEMATICS, APPLIED | HAMILTONIAN OPERATORS | HYDRODYNAMIC TYPE | PHYSICS, MATHEMATICAL | Mathematics

Deformations of Poisson structures | Poisson cohomology | Poisson brackets of hydrodynamic type | Mathematical Physics | Physics and Astronomy(all) | Geometry and Topology | MATHEMATICS, APPLIED | HAMILTONIAN OPERATORS | HYDRODYNAMIC TYPE | PHYSICS, MATHEMATICAL | Mathematics

Journal Article

Physica. D, ISSN 0167-2789, 2016, Volume 335, pp. 54 - 69

...: an energy functional and a Poisson bracket. The goal of this paper is to elucidate how the Poisson brackets can be constructed and what additional features we also gain by the construction...

Non-equilibrium thermodynamics | Hierarchy | Poisson bracket | Projection | GENERIC | Lie–Poisson equation | COMPLEX FLUIDS | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | RHEOLOGY | Lie-Poisson equation | PRINCIPLE | FORMULATION | PHYSICS, MATHEMATICAL | KINETIC-THEORY | GENERAL FORMALISM | DYNAMICS | DIFFUSION | Thermodynamics

Non-equilibrium thermodynamics | Hierarchy | Poisson bracket | Projection | GENERIC | Lie–Poisson equation | COMPLEX FLUIDS | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | RHEOLOGY | Lie-Poisson equation | PRINCIPLE | FORMULATION | PHYSICS, MATHEMATICAL | KINETIC-THEORY | GENERAL FORMALISM | DYNAMICS | DIFFUSION | Thermodynamics

Journal Article

Physics of plasmas, ISSN 1089-7674, 2016, Volume 23, Issue 6, p. 062101

... of deriving the noncanonical Poisson brackets used in their Hamiltonian formulations. We present fully Lagrangian actions for each, as opposed to the fully Eulerian, or mixed Eulerian-Lagrangian, actions that have appeared previously...

FLUIDS | PLASMA DYNAMICS | VARIATIONAL PRINCIPLE | WAVES | VLASOV EQUATION | PHYSICS, FLUIDS & PLASMAS | HYDRODYNAMICS | POISSON BRACKETS | ACTION PRINCIPLE FORMULATIONS

FLUIDS | PLASMA DYNAMICS | VARIATIONAL PRINCIPLE | WAVES | VLASOV EQUATION | PHYSICS, FLUIDS & PLASMAS | HYDRODYNAMICS | POISSON BRACKETS | ACTION PRINCIPLE FORMULATIONS

Journal Article

Nuclear Physics, Section A, ISSN 0375-9474, 2010, Volume 844, Issue 1, pp. 95c - 108c

In this article we give a concise review of recent progress in our understanding of the Lie 3-algebra and their application to the Bagger-Lambert-Gustavsson...

POISSON | PHYSICS, NUCLEAR | COVARIANT ACTION | Physics - High Energy Physics - Theory

POISSON | PHYSICS, NUCLEAR | COVARIANT ACTION | Physics - High Energy Physics - Theory

Journal Article

Modern Physics Letters A, ISSN 0217-7323, 06/2017, Volume 32, Issue 19, p. 1750100

.... A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler...

Peierls brackets | covariant formalism | field theory | PHYSICS, NUCLEAR | POISSON BRACKETS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Peierls brackets | covariant formalism | field theory | PHYSICS, NUCLEAR | POISSON BRACKETS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, 04/2019, Volume 26, Issue 2, pp. 202 - 213

A method for the construction of classes of examples of multi-dimensional, multi-component Dubrovin-Novikov brackets of hydrodynamic type is given...

Hamiltonian structures | integrable systems | MATHEMATICS, APPLIED | CLASSIFICATION | POISSON BRACKETS | PHYSICS, MATHEMATICAL

Hamiltonian structures | integrable systems | MATHEMATICS, APPLIED | CLASSIFICATION | POISSON BRACKETS | PHYSICS, MATHEMATICAL

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 06/2017, Volume 116, pp. 330 - 344

We detail the construction of a weak Poisson bracket over a submanifold Σ of a smooth manifold M with respect to a local foliation of this submanifold...

Master equation | Homotopy Poisson algebra | Weak Poisson and Koszul brackets | BRST theory | Gauge system | MATHEMATICS | PHYSICS, MATHEMATICAL | Algebra | Measuring instruments

Master equation | Homotopy Poisson algebra | Weak Poisson and Koszul brackets | BRST theory | Gauge system | MATHEMATICS | PHYSICS, MATHEMATICAL | Algebra | Measuring instruments

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2018, Volume 23, Issue 6, pp. 720 - 734

.... We generalize this system and the related Poisson brackets to higher dimensions. These more general systems are parametrized by lines in projective space...

Poisson structures | 37J35 | Mathematics | Dynamical Systems and Ergodic Theory | Plücker relations | 53D17 | MATHEMATICS, APPLIED | MECHANICS | Plucker relations | PHYSICS, MATHEMATICAL | DYNAMICAL-SYSTEMS

Poisson structures | 37J35 | Mathematics | Dynamical Systems and Ergodic Theory | Plücker relations | 53D17 | MATHEMATICS, APPLIED | MECHANICS | Plucker relations | PHYSICS, MATHEMATICAL | DYNAMICAL-SYSTEMS

Journal Article

The Journal of chemical physics, ISSN 1089-7690, 2014, Volume 140, Issue 18, p. 184106

.... The Poisson bracket mapping equation (PBME) utilizes a partial Wigner transform and a mapping representation for its formulation, and has been developed to describe nonadiabatic processes in an efficient manner...

REDUCED DENSITY-MATRICES | MOLECULAR-DYNAMICS | PHYSIOLOGICAL TEMPERATURE | CRYPTOPHYTE PHYCOCYANIN 645 | MATTHEWS-OLSON COMPLEX | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | QUANTUM-CLASSICAL DYNAMICS | SPIN-BOSON PROBLEM | ZERO-POINT ENERGY | EXCITATION-ENERGY TRANSFER | DEBYE SPECTRAL DENSITY | Thermodynamics | Quantum Theory | Algorithms | Energy Transfer | Models, Chemical | Computer Simulation | Energy flow | Computer simulation | Molecular dynamics | Mapping | Equations of motion | Photosynthesis | Complex systems | MOLECULAR DYNAMICS METHOD | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUATIONS OF MOTION | HAMILTONIANS | POISSON EQUATION | BOSONS | ACCURACY

REDUCED DENSITY-MATRICES | MOLECULAR-DYNAMICS | PHYSIOLOGICAL TEMPERATURE | CRYPTOPHYTE PHYCOCYANIN 645 | MATTHEWS-OLSON COMPLEX | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | QUANTUM-CLASSICAL DYNAMICS | SPIN-BOSON PROBLEM | ZERO-POINT ENERGY | EXCITATION-ENERGY TRANSFER | DEBYE SPECTRAL DENSITY | Thermodynamics | Quantum Theory | Algorithms | Energy Transfer | Models, Chemical | Computer Simulation | Energy flow | Computer simulation | Molecular dynamics | Mapping | Equations of motion | Photosynthesis | Complex systems | MOLECULAR DYNAMICS METHOD | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUATIONS OF MOTION | HAMILTONIANS | POISSON EQUATION | BOSONS | ACCURACY

Journal Article

Indagationes Mathematicae, ISSN 0019-3577, 10/2014, Volume 25, Issue 5, pp. 846 - 871

.... To such a Poisson structure we associate a polyhedral cone and a constant Poisson bracket on this cone...

Poisson Geometry | Gelfand–Zeitlin integrable system | Gelfand-Zeitlin integrable system | Poisson geometry | MATHEMATICS | LIE-GROUPS | Mathematics - Symplectic Geometry

Poisson Geometry | Gelfand–Zeitlin integrable system | Gelfand-Zeitlin integrable system | Poisson geometry | MATHEMATICS | LIE-GROUPS | Mathematics - Symplectic Geometry

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 08/2016, Volume 13, Issue 7

... to the equations of motion. Our results resemble the Peierls-DeWitt bracket that has been analyzed in the multisymplectic context...

Poisson structures | Deformation quantization | field theory | MECHANICS | PHASE-SPACE | NONLINEAR-SYSTEMS | ALGEBRA | QUANTUM-FIELD THEORY | PHYSICS, MATHEMATICAL

Poisson structures | Deformation quantization | field theory | MECHANICS | PHASE-SPACE | NONLINEAR-SYSTEMS | ALGEBRA | QUANTUM-FIELD THEORY | PHYSICS, MATHEMATICAL

Journal Article

18.
Full Text
Elliptic singularities on log symplectic manifolds and Feigin-Odesskii Poisson brackets

Compositio Mathematica, ISSN 0010-437X, 04/2017, Volume 153, Issue 4, pp. 717 - 744

...). Our main application is to the classification of Poisson brackets on Fano fourfolds. For example, we show that Feigin and Odesskii's Poisson structures of type q(5,1) are the only log symplectic structures on projective four-space whose singular points are all elliptic.

logarithmic differential form | elliptic curve | Fano manifold | Poisson structure | hypersurface singularity | MATHEMATICS | HILBERT SCHEMES | FOLIATIONS | DEFORMATIONS | GEOMETRY

logarithmic differential form | elliptic curve | Fano manifold | Poisson structure | hypersurface singularity | MATHEMATICS | HILBERT SCHEMES | FOLIATIONS | DEFORMATIONS | GEOMETRY

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2016, Volume 21, Issue 6, pp. 682 - 696

In this paper, we present Poisson brackets of certain classes of mappings obtained as general periodic reductions of integrable lattice equations...

39A20 | periodic reduction | Lagrangian | 39A14 | 70H06 | Poisson bracket | Mathematics | Dynamical Systems and Ergodic Theory | lattice equation | 70H15 | MATHEMATICS, APPLIED | INTEGRABLE MAPPINGS | MECHANICS | HIROTA | SYSTEMS | PHYSICS, MATHEMATICAL | Lattice theory | Research | Mathematical research | Mappings (Mathematics) | Physics - Exactly Solvable and Integrable Systems

39A20 | periodic reduction | Lagrangian | 39A14 | 70H06 | Poisson bracket | Mathematics | Dynamical Systems and Ergodic Theory | lattice equation | 70H15 | MATHEMATICS, APPLIED | INTEGRABLE MAPPINGS | MECHANICS | HIROTA | SYSTEMS | PHYSICS, MATHEMATICAL | Lattice theory | Research | Mathematical research | Mappings (Mathematics) | Physics - Exactly Solvable and Integrable Systems

Journal Article

1993, Translations of mathematical monographs, ISBN 0821845969, Volume 119., xi, 366

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