06424nam 22018015 450 991015475190332120190708092533.01-4008-8173-010.1515/9781400881734(CKB)3710000000620153(SSID)ssj0001651298(PQKBManifestationID)16426299(PQKBTitleCode)TC0001651298(PQKBWorkID)13112387(PQKB)10989899(MiAaPQ)EBC4738569(DE-B1597)467946(OCoLC)979580786(OCoLC)990460718(DE-B1597)9781400881734(EXLCZ)99371000000062015320190708d2016 fg engurcnu||||||||txtccrLie Equations, Vol. I General Theory. (AM-73) /Donald Clayton Spencer, Antonio KumperaPrinceton, NJ : Princeton University Press, [2016]©19731 online resource (312 pages)Annals of Mathematics Studies ;274Bibliographic Level Mode of Issuance: Monograph0-691-08111-5 Includes bibliographical references and index.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 -- IndexIn 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.Annals of mathematics studies ;Number 73.Lie groupsLie algebrasDifferential equationsAdjoint 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.Lie groups.Lie algebras.Differential equations.512/.55Kumpera Antonio, 103877Spencer Donald Clayton, DE-B1597DE-B1597BOOK9910154751903321Lie Equations, Vol. I2787595UNINA