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

• Autore: Kumpera Antonio
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1973
• Descrizione fisica: 1 online resource (312 pages)
• Disciplina: 512/.55
• Soggetto topico: Lie groups; Lie algebras; Differential equations
• Soggetto non controllato: Adjoint representation; Adjoint; Affine transformation; Alexander Grothendieck; Analytic function; Associative algebra; Atlas (topology); Automorphism; Bernhard Riemann; Big O notation; Bundle map; Category of topological spaces; Cauchy–Riemann equations; Coefficient; Commutative diagram; Commutator; Complex conjugate; Complex group; Complex manifold; Computation; Conformal map; Continuous function; Coordinate system; Corollary; Cotangent bundle; Curvature tensor; Deformation theory; Derivative; Diagonal; Diffeomorphism; Differentiable function; Differential form; Differential operator; Differential structure; Direct proof; Direct sum; Ellipse; Endomorphism; Equation; Exact sequence; Exactness; Existential quantification; Exponential function; Exponential map (Riemannian geometry); Exterior derivative; Fiber bundle; Fibration; Frame bundle; Frobenius theorem (differential topology); Frobenius theorem (real division algebras); Group isomorphism; Groupoid; Holomorphic function; Homeomorphism; Integer; J-invariant; Jacobian matrix and determinant; Jet bundle; Linear combination; Linear map; Manifold; Maximal ideal; Model category; Morphism; Nonlinear system; Open set; Parameter; Partial derivative; Partial differential equation; Pointwise; Presheaf (category theory); Pseudo-differential operator; Pseudogroup; Quantity; Regular map (graph theory); Requirement; Riemann surface; Right inverse; Scalar multiplication; Sheaf (mathematics); Special case; Structure tensor; Subalgebra; Subcategory; Subgroup; Submanifold; Subset; Tangent bundle; Tangent space; Tangent vector; Tensor field; Tensor product; Theorem; Torsion tensor; Transpose; Variable (mathematics); Vector bundle; Vector field; Vector space; Volume element
• Persona (resp. second.): SpencerDonald Clayton
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Lie Equations, Vol. I
• ISBN: 1-4008-8173-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154751903321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 73.