The Poisson linearization problem for sl2(C) / Ioan Mărcuț, Florian Zeiser.

Format:

Book

Author/Creator:

Mărcuț, Ioan, 1984- author.

Zeiser, Florian, author.

Series:

Memoirs of the American Mathematical Society ; volume 317, number 1610.

Memoirs of the American Mathematical Society, 0065-9266 ; volume 317, number 1610

Language:

English

Subjects (All):

Symplectic geometry.

Physical Description:

v, 112 pages ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, 2026.

Summary:

"In this paper, we prove a version of Conn's linearization theorem for the Lie algebra . Namely, we show that any Poisson structure whose linear approximation at a zero is isomorphic to the Poisson structure associated to is linearizable.In the first part, we calculate the Poisson cohomology associated to , and we construct bounded homotopy operators for the Poisson complex of multivector fields that are flat at the origin.In the second part, we obtain the linearization result, which works for a more general class of Lie algebras. For the proof, we develop a Nash-Moser method for functions that are flat at a point." -- Provided by publisher.

Contents:

Poisson cohomology - Introduction

The Poisson cohomology of sl2(C)

Flat foliated cohomology of sl2(C)

Homotopy operators for the foliated complex

Flat Poisson cohomology of sl2(C)

The Nash-Moser method - Introduction

A quantitative linearization theorem

The sketch of the Nash-Moser algorithm

Prerequisites

The algorithm

Proof of Theorem

A. Some decompositions of smooth functions on C

B. Fréchet spaces of smooth functions

C. Smoothing operators for flat functions.

Notes:

Includes bibliographical references (pages 111-112).

ISBN:

147047963X

9781470479633

OCLC:

1574563536