scholarly journals Classical and variational Poisson cohomology

2021 ◽  
Author(s):  
Bojko Bakalov ◽  
Alberto De Sole ◽  
Reimundo Heluani ◽  
Victor G. Kac ◽  
Veronica Vignoli
Keyword(s):  
Poisson Cohomology

scholarly journals Poisson cohomology of regular Poisson manifolds

1992 ◽  
Vol 42 (4) ◽  
pp. 967-988 ◽  
Author(s):  
Ping Xu
Keyword(s):  
Poisson Manifolds ◽  
Poisson Cohomology

scholarly journals On Theory of logarithmic Poisson Cohomology

2017 ◽  
Vol 9 (4) ◽  
pp. 209
Author(s):  
Joseph Dongho ◽  
Alphonse Mbah ◽  
Shuntah Roland Yotcha
Keyword(s):  
Lie Algebra ◽  
Poisson Structure ◽  
Commutative Algebra ◽  
Linear Representation ◽  
Poisson Cohomology ◽  
Associative Commutative Algebra

We define the notion of logarithmic Poisson structure along a non zero ideal $\cali$ of an associative, commutative algebra $\cal A$ and prove that each logarithmic Poisson structure induce a skew symmetric 2-form and a Lie-Rinehart structure on the $\cal A$-module $\Omega_K(\log \cali)$ of logarithmic K\"{a}hler differential. This Lie-Rinehart structure define a representation of the underline Lie algebra. Applying the machinery of Chevaley-Eilenberg and Palais, we define the notion of logarithmic Poisson cohomology which is a measure obstructions of Linear representation of the underline Lie algebra for which the grown ring act by multiplication.

EQUIVARIANT POISSON COHOMOLOGY AND A SPECTRAL SEQUENCE ASSOCIATED WITH A MOMENT MAP

1999 ◽  
Vol 10 (08) ◽  
pp. 977-1010 ◽  
Author(s):  
VIKTOR L. GINZBURG
Keyword(s):  
Tensor Product ◽  
Spectral Sequence ◽  
Vector Fields ◽  
Equivariant Cohomology ◽  
Poisson Manifold ◽  
Momentum Mapping ◽  
Poisson Cohomology ◽  
Leray Spectral Sequence ◽  
Differential Complex ◽  
Extensive Introduction

We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The spectral sequence converges to the Poisson cohomology of the manifold and has the E2-term equal to the tensor product of the cohomology of the Lie algebra and the equivariant Poisson cohomology of the manifold. The latter is defined as the equivariant cohomology of the multi-vector fields made into a G-differential complex by means of the momentum mapping. An extensive introduction to equivariant cohomology of G-differential complexes is given including some new results and a number of examples and applications are considered.

scholarly journals Poisson Cohomology of the Affine Plane

2002 ◽  
Vol 251 (1) ◽  
pp. 448-460 ◽  
Author(s):  
Claude Roger ◽  
Pol Vanhaecke
Keyword(s):  
Affine Plane ◽  
Poisson Cohomology

scholarly journals Remarks on the Lichnerowicz-Poisson cohomology

1990 ◽  
Vol 40 (4) ◽  
pp. 951-963 ◽  
Author(s):  
Izu Vaisman
Keyword(s):  
Poisson Cohomology

scholarly journals On (co)homology of Frobenius Poisson algebras

2014 ◽  
Vol 14 (2) ◽  
pp. 371-386 ◽  
Author(s):  
Can Zhu ◽  
Fred Van Oystaeyen ◽  
Yinhuo Zhang
Keyword(s):  
Bilinear Form ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Poisson Algebra ◽  
Hochschild Homology ◽  
Poisson Algebras ◽  
Poisson Homology ◽  
Poisson Cohomology ◽  
Frobenius Algebras

AbstractIn 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 Poisson cohomology of Frobenius Poisson algebras, similar to that between Hochschild homology and Hochschild cohomology of Frobenius algebras. Then we use the non-degenerate bilinear form on a unimodular Frobenius Poisson algebra to construct a Batalin-Vilkovisky structure on the Poisson cohomology ring making it into a Batalin-Vilkovisky algebra.

MOMENTUM MAPPINGS AND POISSON COHOMOLOGY

1996 ◽  
Vol 07 (03) ◽  
pp. 329-358 ◽  
Author(s):  
VIKTOR L. GINZBURG
Keyword(s):  
Poisson Structure ◽  
Poisson Manifold ◽  
Existence Problem ◽  
Necessary And Sufficient Condition ◽  
Momentum Mapping ◽  
Lie Algebra Cohomology ◽  
Poisson Cohomology ◽  
Poisson Actions ◽  
Poisson Lie Groups ◽  
Necessary And Sufficient

We analyze the question of existence and uniqueness of equivariant momentum mappings for Poisson actions of Poisson Lie groups. A necessary and sufficient condition for the equivariant momentum mapping to be unique is given. The existence problem is solved under some extra hypotheses, for example, when the action preserves the Poisson structure. In this case, the problem is closely related to the triviality of the induced group action on the Poisson cohomology. This action is shown to be trivial whenever the group is compact or semisimple. Conceptually, these results rely upon a version of “Poisson calculus” developed here to make one-forms on a Poisson manifold induce a “flow” preserving the Poisson structure. In the general case, obstructions to the existence of an infinitesimal version of an equivariant momentum mapping are found. Using Lie algebra cohomology with coefficients in Fréchet modules, we show that the obstructions vanish, and the infinitesimal mapping exists, when the group is compact semisimple. We also prove the rigidity of compact group actions preserving the Poisson structure on a compact manifold and calculate the Poisson cohomology of the Poisson homogeneous space [Formula: see text].

scholarly journals Formal Poisson cohomology of twisted r-matrix induced structures

2008 ◽  
Vol 165 (1) ◽  
pp. 381-411 ◽  
Author(s):  
Mourad Ammar ◽  
Norbert Poncin
Keyword(s):  
R Matrix ◽  
Poisson Cohomology
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