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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
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
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 9/2017, Volume 107, Issue 9, pp. 1715 - 1740
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
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
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
Journal Article
Regular and Chaotic Dynamics, ISSN 1560-3547, 1/2018, Volume 23, Issue 1, pp. 47 - 53
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
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
Journal Article
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
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
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
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
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
Journal Article
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
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
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
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
Journal Article
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