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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
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
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
Journal Article
Letters in Mathematical Physics, ISSN 1573-0530, 2004, Volume 69, Issue 1, pp. 61 - 87
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
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
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 04/2017, Volume 114, pp. 404 - 419
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
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
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
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
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
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
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
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
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
Journal Article
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
Journal Article
Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2016, Volume 21, Issue 6, pp. 682 - 696
Journal Article
1993, Translations of mathematical monographs, ISBN 0821845969, Volume 119., xi, 366
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