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101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aLie Equations, Vol. I $eGeneral Theory. (AM-73) /$fDonald Clayton Spencer, Antonio Kumpera
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1973
215   $a1 online resource (312 pages)
225 0 $aAnnals of Mathematics Studies ;$v274
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08111-5 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tForeword -- $tGlossary of Symbols -- $tTable of Contents -- $tIntroduction -- $tA. Integrability of Lie Structures -- $tB. Deformation Theory of Lie Structures -- $tChapter I. Jet Sheaves and Differential Equations -- $tChapter II. Linear Lie Equations -- $tChapter III. Derivations and Brackets -- $tChapter IV. Non-Linear Complexes -- $tChapter V. Derivations of Jet Forms -- $tAppendix. Lie Groupoids -- $tReferences -- $tIndex
330   $aIn this monograph the authors redevelop the theory systematically using two different approaches. A general mechanism for the deformation of structures on manifolds was developed by Donald Spencer ten years ago. A new version of that theory, based on the differential calculus in the analytic spaces of Grothendieck, was recently given by B. Malgrange. The first approach adopts Malgrange's idea in defining jet sheaves and linear operators, although the brackets and the non-linear theory arc treated in an essentially different manner. The second approach is based on the theory of derivations, and its relationship to the first is clearly explained. The introduction describes examples of Lie equations and known integrability theorems, and gives applications of the theory to be developed in the following chapters and in the subsequent volume.
410  0$aAnnals of mathematics studies ;$vNumber 73.
606   $aLie groups
606   $aLie algebras
606   $aDifferential equations
610   $aAdjoint representation.
610   $aAdjoint.
610   $aAffine transformation.
610   $aAlexander Grothendieck.
610   $aAnalytic function.
610   $aAssociative algebra.
610   $aAtlas (topology).
610   $aAutomorphism.
610   $aBernhard Riemann.
610   $aBig O notation.
610   $aBundle map.
610   $aCategory of topological spaces.
610   $aCauchy?Riemann equations.
610   $aCoefficient.
610   $aCommutative diagram.
610   $aCommutator.
610   $aComplex conjugate.
610   $aComplex group.
610   $aComplex manifold.
610   $aComputation.
610   $aConformal map.
610   $aContinuous function.
610   $aCoordinate system.
610   $aCorollary.
610   $aCotangent bundle.
610   $aCurvature tensor.
610   $aDeformation theory.
610   $aDerivative.
610   $aDiagonal.
610   $aDiffeomorphism.
610   $aDifferentiable function.
610   $aDifferential form.
610   $aDifferential operator.
610   $aDifferential structure.
610   $aDirect proof.
610   $aDirect sum.
610   $aEllipse.
610   $aEndomorphism.
610   $aEquation.
610   $aExact sequence.
610   $aExactness.
610   $aExistential quantification.
610   $aExponential function.
610   $aExponential map (Riemannian geometry).
610   $aExterior derivative.
610   $aFiber bundle.
610   $aFibration.
610   $aFrame bundle.
610   $aFrobenius theorem (differential topology).
610   $aFrobenius theorem (real division algebras).
610   $aGroup isomorphism.
610   $aGroupoid.
610   $aHolomorphic function.
610   $aHomeomorphism.
610   $aInteger.
610   $aJ-invariant.
610   $aJacobian matrix and determinant.
610   $aJet bundle.
610   $aLinear combination.
610   $aLinear map.
610   $aManifold.
610   $aMaximal ideal.
610   $aModel category.
610   $aMorphism.
610   $aNonlinear system.
610   $aOpen set.
610   $aParameter.
610   $aPartial derivative.
610   $aPartial differential equation.
610   $aPointwise.
610   $aPresheaf (category theory).
610   $aPseudo-differential operator.
610   $aPseudogroup.
610   $aQuantity.
610   $aRegular map (graph theory).
610   $aRequirement.
610   $aRiemann surface.
610   $aRight inverse.
610   $aScalar multiplication.
610   $aSheaf (mathematics).
610   $aSpecial case.
610   $aStructure tensor.
610   $aSubalgebra.
610   $aSubcategory.
610   $aSubgroup.
610   $aSubmanifold.
610   $aSubset.
610   $aTangent bundle.
610   $aTangent space.
610   $aTangent vector.
610   $aTensor field.
610   $aTensor product.
610   $aTheorem.
610   $aTorsion tensor.
610   $aTranspose.
610   $aVariable (mathematics).
610   $aVector bundle.
610   $aVector field.
610   $aVector space.
610   $aVolume element.
615  0$aLie groups.
615  0$aLie algebras.
615  0$aDifferential equations.
676   $a512/.55
700   $aKumpera$b Antonio, $0103877
702   $aSpencer$b Donald Clayton, 
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154751903321
996   $aLie Equations, Vol. I$92787595
997   $aUNINA