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Poisson cohomology of "book" Poisson structures

Henrique Bursztyn, Hudson Lima

Abstract

We compute the Poisson cohomology of the linear Poisson structure dual to the n-dimensional "book" Lie algebra, defined by [e_0,e_i]=e_i, [e_i,e_j]=0, for i,j=1,...,n-1.

Poisson cohomology of "book" Poisson structures

Abstract

We compute the Poisson cohomology of the linear Poisson structure dual to the n-dimensional "book" Lie algebra, defined by [e_0,e_i]=e_i, [e_i,e_j]=0, for i,j=1,...,n-1.
Paper Structure (9 sections, 16 theorems, 125 equations, 1 figure)

This paper contains 9 sections, 16 theorems, 125 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Book Poisson cohomology
  3. Proofs of the main results
  4. The complex $(\mathcal{C}^\bullet_\mathcal{I}, \delta)$
  5. The quasi-isomorphism
  6. Dimensions
  7. Basis for the book cohomology
  8. Taylor Series and the Euler vector field
  9. Proof of Lemma \ref{['lem:timeDependent_flatness']}

Key Result

Lemma 2.1

Let $\mu = \partial_t\wedge a + b \in \mathfrak{X}^k(U)$, as in eq:mudecomp. Then

Figures (1)

  • Figure 1: Leaves of $\Lambda_{book}$

Theorems & Definitions (31)

  • Lemma 2.1
  • proof
  • Theorem 2.3
  • Example 2.4
  • Example 2.5
  • Definition 2.6
  • Theorem 2.7
  • Lemma 3.1
  • Proposition 3.2
  • proof
  • ...and 21 more