Journal of Algebra, ISSN 0021-8693, 11/2015, Volume 442, pp. 484 - 505

A version of the twisted Poincaré duality is proved between the Poisson homology and cohomology of a polynomial Poisson algebra with values in an arbitrary...

Poisson algebras | Poincaré duality | Modular class | Poisson (co)homology | MATHEMATICS | ALGEBRAS | COMPLEX | Poincare duality | Algebra

Poisson algebras | Poincaré duality | Modular class | Poisson (co)homology | MATHEMATICS | ALGEBRAS | COMPLEX | Poincare duality | Algebra

Journal Article

Journal of K-Theory, ISSN 1865-2433, 06/2014, Volume 14, Issue 2, pp. 371 - 386

In this paper, we study Poisson (co)homology of a Frobenius Poisson algebra. More precisely, we show that there exists a duality between Poisson homology and...

BV algebra | Frobenius algebra | Poisson algebra | duality | Poisson (co)homology | MATHEMATICS | COHOMOLOGY

BV algebra | Frobenius algebra | Poisson algebra | duality | Poisson (co)homology | MATHEMATICS | COHOMOLOGY

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 9/2017, Volume 107, Issue 9, pp. 1715 - 1740

In this paper, we show that the twisted Poincaré duality between Poisson homology and cohomology can be derived from the Serre invertible bimodule. This gives...

Calabi–Yau algebra | Theoretical, Mathematical and Computational Physics | Complex Systems | Poisson (co)homology | Physics | Hochschild (co)homology | Geometry | Dualizing complex | 16E40 | 17B35 | 17B63 | Group Theory and Generalizations | Poisson algebra | HOPF-ALGEBRAS | RINGS | Poisson (co) homology | POINCARE-DUALITY | PHYSICS, MATHEMATICAL | DUALIZING COMPLEXES | Hochschild (co) homology | UNIVERSAL ENVELOPING-ALGEBRAS | COHOMOLOGY | Calabi-Yau algebra | MANIFOLD | Algebra | Mathematics - Rings and Algebras

Calabi–Yau algebra | Theoretical, Mathematical and Computational Physics | Complex Systems | Poisson (co)homology | Physics | Hochschild (co)homology | Geometry | Dualizing complex | 16E40 | 17B35 | 17B63 | Group Theory and Generalizations | Poisson algebra | HOPF-ALGEBRAS | RINGS | Poisson (co) homology | POINCARE-DUALITY | PHYSICS, MATHEMATICAL | DUALIZING COMPLEXES | Hochschild (co) homology | UNIVERSAL ENVELOPING-ALGEBRAS | COHOMOLOGY | Calabi-Yau algebra | MANIFOLD | Algebra | Mathematics - Rings and Algebras

Journal Article

Journal of Algebra, ISSN 0021-8693, 2009, Volume 322, Issue 4, pp. 1151 - 1169

In this paper, we compute the Poisson (co)homology of a polynomial Poisson structure given by two Casimir polynomial functions which define a complete...

Poisson structures | Casimir functions | Poisson (co)homology | Unimodular Poisson structure | Complete intersection with an isolated singularity | MATHEMATICS

Poisson structures | Casimir functions | Poisson (co)homology | Unimodular Poisson structure | Complete intersection with an isolated singularity | MATHEMATICS

Journal Article

Journal of Algebra, ISSN 0021-8693, 2006, Volume 299, Issue 2, pp. 747 - 777

To each polynomial φ ∈ F [ x , y , z ] is associated a Poisson structure on F 3 , a surface and a Poisson structure on this surface. When φ is weight...

Isolated singularities | Poisson homology | Poisson cohomology | MATHEMATICS | COHOMOLOGY | isolated singularities | PLANE | MANIFOLDS | Mathematics - Quantum Algebra | Quantum Algebra | Mathematics

Isolated singularities | Poisson homology | Poisson cohomology | MATHEMATICS | COHOMOLOGY | isolated singularities | PLANE | MANIFOLDS | Mathematics - Quantum Algebra | Quantum Algebra | Mathematics

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 01/2020, Volume 147, p. 103522

In this paper, we study the gravity algebra structure on the negative cyclic homology or the cyclic cohomology of several classes of algebras. These algebras...

Cyclic homology | Batalin–Vilkovisky | Deformation quantization | Unimodular Poisson | Calabi–Yau | Calabi-Yau | OPERADS | MATHEMATICS | FORMALITY | COHOMOLOGY | Batalin-Vilkovisky | BATALIN-VILKOVISKY ALGEBRA | DUALITY | PHYSICS, MATHEMATICAL

Cyclic homology | Batalin–Vilkovisky | Deformation quantization | Unimodular Poisson | Calabi–Yau | Calabi-Yau | OPERADS | MATHEMATICS | FORMALITY | COHOMOLOGY | Batalin-Vilkovisky | BATALIN-VILKOVISKY ALGEBRA | DUALITY | PHYSICS, MATHEMATICAL

Journal Article

Acta Applicandae Mathematicae, ISSN 0167-8019, 1/2010, Volume 109, Issue 1, pp. 137 - 150

A general theory of the Frölicher–Nijenhuis and Schouten–Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related...

58J10 | Integrability | Theoretical, Mathematical and Computational Physics | Nonlinear differential equations | Mathematics | Algebraic approach | Statistical Physics, Dynamical Systems and Complexity | 58H15 | Hamiltonian formalism | Poisson structures | Frölicher–Nijenhuis bracket | Mechanics | Mathematics, general | Computer Science, general | Schouten–Nijenhuis bracket | Schouten-Nijenhuis bracket | Frölicher-Nijenhuis bracket | Frolicher-Nijenhuis bracket | MATHEMATICS, APPLIED | COMMUTATIVE ALGEBRAS | CALCULUS | DEFORMATIONS | OPERATORS | Studies | Nonlinear equations | Algebra | Differential equations

58J10 | Integrability | Theoretical, Mathematical and Computational Physics | Nonlinear differential equations | Mathematics | Algebraic approach | Statistical Physics, Dynamical Systems and Complexity | 58H15 | Hamiltonian formalism | Poisson structures | Frölicher–Nijenhuis bracket | Mechanics | Mathematics, general | Computer Science, general | Schouten–Nijenhuis bracket | Schouten-Nijenhuis bracket | Frölicher-Nijenhuis bracket | Frolicher-Nijenhuis bracket | MATHEMATICS, APPLIED | COMMUTATIVE ALGEBRAS | CALCULUS | DEFORMATIONS | OPERATORS | Studies | Nonlinear equations | Algebra | Differential equations

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 1/2018, Volume 23, Issue 1, pp. 47 - 53

We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some...

Poisson homology | foliated cohomology | Mathematics | Dynamical Systems and Ergodic Theory | 53C12 | 53D17 | MATHEMATICS, APPLIED | MECHANICS | SINGULARITIES | MODULAR CLASS | PHYSICS, MATHEMATICAL | Manifolds (Mathematics) | Homology theory (Mathematics) | Research | Cohomology theory | Mathematical research | Mathematics - Symplectic Geometry | Geometria diferencial | Geometria | Varietats (Matemàtica) | Matemàtiques i estadística | Àrees temàtiques de la UPC | Physics | Astrophysics

Poisson homology | foliated cohomology | Mathematics | Dynamical Systems and Ergodic Theory | 53C12 | 53D17 | MATHEMATICS, APPLIED | MECHANICS | SINGULARITIES | MODULAR CLASS | PHYSICS, MATHEMATICAL | Manifolds (Mathematics) | Homology theory (Mathematics) | Research | Cohomology theory | Mathematical research | Mathematics - Symplectic Geometry | Geometria diferencial | Geometria | Varietats (Matemàtica) | Matemàtiques i estadística | Àrees temàtiques de la UPC | Physics | Astrophysics

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 4/2019, Volume 14, Issue 2, pp. 395 - 420

This paper is devoted to study Frobenius Poisson algebras. We introduce pseudo-unimodular Poisson algebras by generalizing unimodular Poisson algebras, and...

Batalin-Vilkovisky algebra | 16E40 | modular derivation | 17B40 | 17B63 | Poisson (co)homology | Mathematics, general | Mathematics | Poisson algebra | Frobenius algebra | MATHEMATICS | Operators (mathematics) | Homology | Polynomials | Algebra | Mathematical analysis | Modular structures

Batalin-Vilkovisky algebra | 16E40 | modular derivation | 17B40 | 17B63 | Poisson (co)homology | Mathematics, general | Mathematics | Poisson algebra | Frobenius algebra | MATHEMATICS | Operators (mathematics) | Homology | Polynomials | Algebra | Mathematical analysis | Modular structures

Journal Article

Journal of Algebra, ISSN 0021-8693, 2009, Volume 322, Issue 10, pp. 3580 - 3613

Let g be a finite-dimensional semi-simple Lie algebra, h a Cartan subalgebra of g , and W its Weyl group. The group W acts diagonally on V : = h ⊕ h ∗ , as...

Weyl group | Berest–Etingof–Ginzburg equation | Poisson homology | Pfaff | Alev's conjecture | Invariants | Berest-Etingof-Ginzburg equation | MATHEMATICS | WEYL ALGEBRA

Weyl group | Berest–Etingof–Ginzburg equation | Poisson homology | Pfaff | Alev's conjecture | Invariants | Berest-Etingof-Ginzburg equation | MATHEMATICS | WEYL ALGEBRA

Journal Article

11.
Full Text
Twisted Poincaré duality for Poisson homology and cohomology of affine Poisson algebras

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2015, Volume 143, Issue 5, pp. 1957 - 1967

This paper investigates the Poisson (co)homology of affine Poisson algebras. It is shown that there is a twisted Poincare duality between their Poisson...

Poincaré duality | Poisson (co)homology | Affine Poisson algebra | Enveloping algebra | Hochschild (co)homology | MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX | Poincare duality | enveloping algebra

Poincaré duality | Poisson (co)homology | Affine Poisson algebra | Enveloping algebra | Hochschild (co)homology | MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX | Poincare duality | enveloping algebra

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 2/2007, Volume 79, Issue 2, pp. 161 - 174

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra $${R={\mathbb...

Geometry | 17B55 | 16E40 | Poincaré duality | 17B63 | Mathematical and Computational Physics | Poisson (co)homology | Group Theory and Generalizations | 17B37 | Physics | Statistical Physics | Hochschild (co)homology | COHOMOLOGY | QUANTUM GROUPS | Poincare duality | KOSZUL | MODULAR CLASS | HOCHSCHILD HOMOLOGY | PHYSICS, MATHEMATICAL

Geometry | 17B55 | 16E40 | Poincaré duality | 17B63 | Mathematical and Computational Physics | Poisson (co)homology | Group Theory and Generalizations | 17B37 | Physics | Statistical Physics | Hochschild (co)homology | COHOMOLOGY | QUANTUM GROUPS | Poincare duality | KOSZUL | MODULAR CLASS | HOCHSCHILD HOMOLOGY | PHYSICS, MATHEMATICAL

Journal Article

Journal fur die Reine und Angewandte Mathematik, ISSN 0075-4102, 04/2006, Volume 593, Issue 593, pp. 117 - 168

In this article, the cyclic homology theory of formal deformation quantizations of the convolution algebra associated to a proper etale Lie groupoid is...

MATHEMATICS | POISSON MANIFOLDS | INDEX THEOREM | ORBIFOLDS | QUANTIZATION

MATHEMATICS | POISSON MANIFOLDS | INDEX THEOREM | ORBIFOLDS | QUANTIZATION

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 05/2011, Volume 86, Issue 8, pp. 1041 - 1068

The simultaneous use of a pair of complementary discrete formulations for electrostatic boundary value problems (BVPs) allows to accurately compute...

finite integration technique (FIT) | cell method (CM) | thick links | electrostatics | (Co)homology | complementarity | discrete geometric approach (DGA) | Discrete geometric approach (DGA) | Complementarity | Cell method (CM) | Finite integration technique (FIT) | Thick links | Electrostatics | MIMETIC DISCRETIZATIONS | NEUTRAL BEAM INJECTOR | BOUNDARY-ELEMENT METHOD | FIELD PROBLEMS | ELLIPTIC PROBLEMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | ELECTROMAGNETIC THEORY | FINITE-ELEMENT | POISSON EQUATIONS | EDDY-CURRENT FORMULATION | ALGEBRAIC FORMULATION | Boundary value problems | Algorithms | Computation | Mathematical analysis | Mathematical models | Vector potentials | Three dimensional

finite integration technique (FIT) | cell method (CM) | thick links | electrostatics | (Co)homology | complementarity | discrete geometric approach (DGA) | Discrete geometric approach (DGA) | Complementarity | Cell method (CM) | Finite integration technique (FIT) | Thick links | Electrostatics | MIMETIC DISCRETIZATIONS | NEUTRAL BEAM INJECTOR | BOUNDARY-ELEMENT METHOD | FIELD PROBLEMS | ELLIPTIC PROBLEMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | ELECTROMAGNETIC THEORY | FINITE-ELEMENT | POISSON EQUATIONS | EDDY-CURRENT FORMULATION | ALGEBRAIC FORMULATION | Boundary value problems | Algorithms | Computation | Mathematical analysis | Mathematical models | Vector potentials | Three dimensional

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 22, pp. 11694 - 11744

In this article, we show under what additional ingredients a comp (or opposite) module over an operad with multiplication can be given the structure of a...

MATHEMATICS | ALGEBRAS | COHOMOLOGY | BIALGEBROIDS | HOMOLOGY

MATHEMATICS | ALGEBRAS | COHOMOLOGY | BIALGEBROIDS | HOMOLOGY

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2008, Volume 4, p. 064

Within the framework of deformation quantization, a first step towards the study of star-products is the calculation of Hochschild cohomology. The aim of this...

Quantization | Groebner bases | Hochschild cohomology | Klein surfaces | Hochschild homology | Star-products | POISSON COHOMOLOGY | star-products | SINGULARITIES | INVARIANTS | PHYSICS, MATHEMATICAL | DEFORMATION-THEORY | quantization

Quantization | Groebner bases | Hochschild cohomology | Klein surfaces | Hochschild homology | Star-products | POISSON COHOMOLOGY | star-products | SINGULARITIES | INVARIANTS | PHYSICS, MATHEMATICAL | DEFORMATION-THEORY | quantization

Journal Article

17.
Full Text
Homological properties of certain Generalized Jacobian Poisson Structures in dimension 3

Journal of Geometry and Physics, ISSN 0393-0440, 2011, Volume 61, Issue 12, pp. 2352 - 2368

The unimodularity condition for a Poisson structure (i.e., a Poisson structure with a trivial modular class) induces a Poincaré duality between its Poisson...

Poincaré duality | Modular class | Generalazed Jacobian Poisson structures | Poisson (co)homology | MATHEMATICS, APPLIED | COMPLEX | COHOMOLOGY | SKLYANIN ALGEBRAS | Poincare duality | MANIFOLDS | PHYSICS, MATHEMATICAL

Poincaré duality | Modular class | Generalazed Jacobian Poisson structures | Poisson (co)homology | MATHEMATICS, APPLIED | COMPLEX | COHOMOLOGY | SKLYANIN ALGEBRAS | Poincare duality | MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

Bulletin of the Brazilian Mathematical Society, ISSN 1678-7544, 12/2011, Volume 42, Issue 4, pp. 783 - 803

Hans Duistermaat was scheduled to lecture in the 2010 School on Poisson Geometry at IMPA, but passed away suddenly. This is a record of a talk I gave at the...

Poisson geometry | Hamiltonian dynamics | ELLIPTIC OPERATORS | BRACKETS | MONODROMY | INTEGRABILITY | DIFFERENTIAL-EQUATIONS | FORMULA | CO-HOMOLOGY | MATHEMATICS | INTEGRATION | SPHERICAL PENDULUM | MANIFOLDS

Poisson geometry | Hamiltonian dynamics | ELLIPTIC OPERATORS | BRACKETS | MONODROMY | INTEGRABILITY | DIFFERENTIAL-EQUATIONS | FORMULA | CO-HOMOLOGY | MATHEMATICS | INTEGRATION | SPHERICAL PENDULUM | MANIFOLDS

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 3/2009, Volume 87, Issue 3, pp. 267 - 281

In this paper, we compute the Hochschild homology of elliptic Sklyanin algebras. These algebras are deformations of polynomial algebra with a Poisson bracket...

Geometry | 16E40 | quantum space | 17B63 | Mathematical and Computational Physics | deformation | Poisson homology | Group Theory and Generalizations | Hochschild homology | Physics | Statistical Physics | Quantum space | Deformation | COHOMOLOGY | POISSON MANIFOLDS | PHYSICS, MATHEMATICAL

Geometry | 16E40 | quantum space | 17B63 | Mathematical and Computational Physics | deformation | Poisson homology | Group Theory and Generalizations | Hochschild homology | Physics | Statistical Physics | Quantum space | Deformation | COHOMOLOGY | POISSON MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

Journal of Physics A: Mathematical and General, ISSN 0305-4470, 01/2003, Volume 36, Issue 1, pp. 161 - 181

Jacobi algebroids (i.e. 'Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies...

BUNDLES | GERSTENHABER ALGEBRAS | DIRAC STRUCTURES | GROUPOIDS | POISSON MANIFOLDS | SYSTEMS | LIE BIALGEBROIDS | PHYSICS, MATHEMATICAL

BUNDLES | GERSTENHABER ALGEBRAS | DIRAC STRUCTURES | GROUPOIDS | POISSON MANIFOLDS | SYSTEMS | LIE BIALGEBROIDS | PHYSICS, MATHEMATICAL

Journal Article

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