Lie Equations, Vol. I : : General Theory. (AM-73) /

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

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...

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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Kumpera, Antonio,
Spencer, Donald Clayton,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1973
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 73
Online Access:
Physical Description:1 online resource (309 p.)
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100 1 |a Kumpera, Antonio,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Lie Equations, Vol. I :  |b General Theory. (AM-73) /  |c Donald Clayton Spencer, Antonio Kumpera. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2016] 
264 4 |c ©1973 
300 |a 1 online resource (309 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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490 0 |a Annals of Mathematics Studies ;  |v 73 
505 0 0 |t Frontmatter --   |t Foreword --   |t Glossary of Symbols --   |t Table of Contents --   |t Introduction --   |t A. Integrability of Lie Structures --   |t B. Deformation Theory of Lie Structures --   |t Chapter I. Jet Sheaves and Differential Equations --   |t Chapter II. Linear Lie Equations --   |t Chapter III. Derivations and Brackets --   |t Chapter IV. Non-Linear Complexes --   |t Chapter V. Derivations of Jet Forms --   |t Appendix. Lie Groupoids --   |t References --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Differential equations. 
650 0 |a Lie algebras. 
650 0 |a Lie groups. 
650 7 |a MATHEMATICS / Algebra / Linear.  |2 bisacsh 
653 |a Adjoint representation. 
653 |a Adjoint. 
653 |a Affine transformation. 
653 |a Alexander Grothendieck. 
653 |a Analytic function. 
653 |a Associative algebra. 
653 |a Atlas (topology). 
653 |a Automorphism. 
653 |a Bernhard Riemann. 
653 |a Big O notation. 
653 |a Bundle map. 
653 |a Category of topological spaces. 
653 |a Cauchy-Riemann equations. 
653 |a Coefficient. 
653 |a Commutative diagram. 
653 |a Commutator. 
653 |a Complex conjugate. 
653 |a Complex group. 
653 |a Complex manifold. 
653 |a Computation. 
653 |a Conformal map. 
653 |a Continuous function. 
653 |a Coordinate system. 
653 |a Corollary. 
653 |a Cotangent bundle. 
653 |a Curvature tensor. 
653 |a Deformation theory. 
653 |a Derivative. 
653 |a Diagonal. 
653 |a Diffeomorphism. 
653 |a Differentiable function. 
653 |a Differential form. 
653 |a Differential operator. 
653 |a Differential structure. 
653 |a Direct proof. 
653 |a Direct sum. 
653 |a Ellipse. 
653 |a Endomorphism. 
653 |a Equation. 
653 |a Exact sequence. 
653 |a Exactness. 
653 |a Existential quantification. 
653 |a Exponential function. 
653 |a Exponential map (Riemannian geometry). 
653 |a Exterior derivative. 
653 |a Fiber bundle. 
653 |a Fibration. 
653 |a Frame bundle. 
653 |a Frobenius theorem (differential topology). 
653 |a Frobenius theorem (real division algebras). 
653 |a Group isomorphism. 
653 |a Groupoid. 
653 |a Holomorphic function. 
653 |a Homeomorphism. 
653 |a Integer. 
653 |a J-invariant. 
653 |a Jacobian matrix and determinant. 
653 |a Jet bundle. 
653 |a Linear combination. 
653 |a Linear map. 
653 |a Manifold. 
653 |a Maximal ideal. 
653 |a Model category. 
653 |a Morphism. 
653 |a Nonlinear system. 
653 |a Open set. 
653 |a Parameter. 
653 |a Partial derivative. 
653 |a Partial differential equation. 
653 |a Pointwise. 
653 |a Presheaf (category theory). 
653 |a Pseudo-differential operator. 
653 |a Pseudogroup. 
653 |a Quantity. 
653 |a Regular map (graph theory). 
653 |a Requirement. 
653 |a Riemann surface. 
653 |a Right inverse. 
653 |a Scalar multiplication. 
653 |a Sheaf (mathematics). 
653 |a Special case. 
653 |a Structure tensor. 
653 |a Subalgebra. 
653 |a Subcategory. 
653 |a Subgroup. 
653 |a Submanifold. 
653 |a Subset. 
653 |a Tangent bundle. 
653 |a Tangent space. 
653 |a Tangent vector. 
653 |a Tensor field. 
653 |a Tensor product. 
653 |a Theorem. 
653 |a Torsion tensor. 
653 |a Transpose. 
653 |a Variable (mathematics). 
653 |a Vector bundle. 
653 |a Vector field. 
653 |a Vector space. 
653 |a Volume element. 
700 1 |a Spencer, Donald Clayton,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Annals of Mathematics eBook-Package 1940-2020  |z 9783110494914  |o ZDB-23-PMB 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Archive 1927-1999  |z 9783110442496 
776 0 |c print  |z 9780691081113 
856 4 0 |u https://doi.org/10.1515/9781400881734 
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856 4 2 |3 Cover  |u https://www.degruyter.com/document/cover/isbn/9781400881734/original 
912 |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999  |c 1927  |d 1999 
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