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Title Lie Equations. Vol. 1, General Theory. (AM-73) / Antonio Kumpera, Donald Clayton Spencer.
Imprint Princeton, NJ : Princeton University Press, [2016]


 Internet  Electronic Book    AVAILABLE
Description 1 online resource.
Series Annals of Mathematics Studies, 0066-2313 ; 73.
Annals of mathematics studies. 0066-2313 ; 73.
Note Available only to authorized UTEP users.
In English.
Online resource; title from PDF title page (publisher's Web site, viewed May 30, 2016).
Subject Differential equations.
Lie algebras.
Lie groups.
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.
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.
Other Author Spencer, D. C. (Donald Clayton), 1912-2001.
Other Title print 9780691081113.