Lie Equations, Vol. I : General Theory. (AM-73) / Donald Clayton Spencer, Antonio Kumpera.

Format:

Book

Author/Creator:

Kumpera, Antonio, author.

Spencer, Donald Clayton, author.

Series:

Annals of mathematics studies ; Number 73.

Annals of Mathematics Studies ; 274

Language:

English

Subjects (All):

Lie groups.

Lie algebras.

Differential equations.

Physical Description:

1 online resource (312 pages).

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

In this monograph the authors redevelop the theory systematically using two different approaches. A general mechanism for the deformation of structures on manifolds was developed by Donald Spencer ten years ago. A new version of that theory, based on the differential calculus in the analytic spaces of Grothendieck, was recently given by B. Malgrange. The first approach adopts Malgrange's idea in defining jet sheaves and linear operators, although the brackets and the non-linear theory arc treated in an essentially different manner. The second approach is based on the theory of derivations, and its relationship to the first is clearly explained. The introduction describes examples of Lie equations and known integrability theorems, and gives applications of the theory to be developed in the following chapters and in the subsequent volume.

Contents:

Frontmatter

Foreword

Glossary of Symbols

Table of Contents

Introduction

A. Integrability of Lie Structures

B. Deformation Theory of Lie Structures

Chapter I. Jet Sheaves and Differential Equations

Chapter II. Linear Lie Equations

Chapter III. Derivations and Brackets

Chapter IV. Non-Linear Complexes

Chapter V. Derivations of Jet Forms

Appendix. Lie Groupoids

References

Index

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400881734

1400881730

OCLC:

979580786