scholarly journals Poisson cohomology, Koszul duality, and Batalin–Vilkovisky algebras

2021 ◽  
Author(s):  
Xiaojun Chen ◽  
Youming Chen ◽  
Farkhod Eshmatov ◽  
Song Yang
Keyword(s):  
Koszul Duality ◽  
Poisson Cohomology

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 KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS

2010 ◽  
Vol 89 (1) ◽  
pp. 23-49 ◽  
Author(s):  
VOLODYMYR MAZORCHUK
Keyword(s):  
Complete Picture ◽  
Projective Modules ◽  
Koszul Duality ◽  
Tilting Theory

AbstractWe give a complete picture of the interaction between the Koszul and Ringel dualities for graded standardly stratified algebras (in the sense of Cline, Parshall and Scott) admitting linear tilting (co)resolutions of standard and proper costandard modules. We single out a certain class of graded standardly stratified algebras, imposing the condition that standard filtrations of projective modules are finite, and develop a tilting theory for such algebras. Under the assumption on existence of linear tilting (co)resolutions we show that algebras from this class are Koszul, that both the Ringel and Koszul duals belong to the same class, and that these two dualities on this class commute.

Erratum to ?Koszul duality for operads,? vol. 76 (1994) pp. 203?272

1995 ◽  
Vol 80 (1) ◽  
pp. 293-293 ◽  
Author(s):  
V. Ginzburg ◽  
M. Kapranov
Keyword(s):  
Koszul Duality

Koszul Duality I

2020 ◽  
pp. 513-527
Author(s):  
Ben Elias ◽  
Shotaro Makisumi ◽  
Ulrich Thiel ◽  
Geordie Williamson
Keyword(s):  
Koszul Duality

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.

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