Lie pseudogroups à la Cartan / Marius Crainic, Ori Yudilevich.

Format:

Book

Author/Creator:

Crainic, Marius, author.

Yudilevich, Ori, author.

Series:

Memoirs of the American Mathematical Society ; v. 1527.

Memoirs of the American Mathematical Society, 0065-9266 ; v. 1527

Language:

English

Subjects (All):

Cartan, Elie, 1869-1951.

Cartan, Elie.

Lie, Sophus, 1842-1899.

Lie, Sophus.

Pseudogroups.

Lie algebroids.

Physical Description:

v, 99 pages ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2024

Summary:

We present a modern formulation of Élie Cartan's structure theory for Lie pseudogroups and prove a reduction theorem that clarifies the role of Cartan's systatic system. The monograph is divided into three parts. In part one, using notions coming from the theory of Lie groupoids and algebroids, we introduce the framework of Cartan algebroids and realizations, structures that encode Cartan's structure equations and notion of a pseudogroup in normal form. In part two, we present a novel proof of Cartan's Second Fundamental Theorem which states that any Lie pseudogroup is equivalent to a pseudogroup in normal form. In part three, we prove a new reduction theorem that states that, under suitable regularity conditions, a pseudogroup in normal form canonically reduces to a generalized pseudogroup of local solutions of a Lie-Pfaffian groupoid.

Contents:

Introduction

Chapter 1. Cartan algebroids, realizations, pseudogroups in normal form

Chapter 2. Cartan's second fundamental theorem

Chapter 3. The systatic space and reduction

Appendix A. Appendix

Bibliography

Index.

Notes:

Includes index and bibliographical references.

ISBN:

1470472651

9781470472658

OCLC:

1477765196