Pommaret J.F. — Systems of partial differential equations and Lie pseudogroups :: Электронная библиотека попечительского совета мехмата МГУ

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Pommaret J.F. — Systems of partial differential equations and Lie pseudogroups

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Название: Systems of partial differential equations and Lie pseudogroups

Автор: Pommaret J.F.

Аннотация:

In mathematics, a pseudogroup is an extension of the group concept, but one that grew out of the geometric approach of Sophus Lie, rather than out of abstract algebra (such as quasigroup, for example). A theory of pseudogroups was developed by Élie Cartan in the early 1900s.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 424

Добавлена в каталог: 05.02.2014

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Предметный указатель

"Flat" mapping      6.5.19
"Sharp" mapping      6.5.19
action      6.1.9
Acyclicity      3.1.10
Affine bundle      1.1.29
Algebraic bracket      7.2.29
Algebraic pseudogroup      7.6.9
Amorphous system      5.2.6
Analytic system      2.3.4
Associated bundle      7.8.1
Automorphic system      7.Pb.5
Automorphism      6.1.18
Base manifold      1.1.3
Bundle      1.1.15
Bundle of geometric objects      7.2.6
Canonical parameters      6.2.14
Cartan — Khaeler theorem      4.4.3
Cauchy — Kowaleski theorem      4.4.6
Cauchy — Riemann equations      7.Pb.3
Center      7.8.21
centralizer      7.8.29
CHARACTER      3.2.5
Characteristic covector      5.6.2
Characteristic variety      5.6.5
Christoffel symbols      1.6.3
class      3.2.2
Classical Lie derivative      6.4.7
Closed subgroup      6.1.7
Coboundary      7.8.22
Cocycle      7.8.22
Connected component      6.1.16
Connected functions      6.3.22
Connected vectors      6.1.24
Cotangent bundle      1.1.22
Covariant derivative      7.8.38
Criterion of formal integrability      2.4.9
Criterion of involutiveness      2.4.11
Deformation cohomology      7.8.22
Deformation of structures      7.7.2
Deformation theory      7.2.24
Dependent vectors      6.1.23
Derivation      7.8.24
Determined system      5.6.6
Diagram chasing      2.2.14
Diffeomorphism      6.1—18
Differential invariant      7.1.44
Discrete group      6.1.3
distribution      6.3.6
Effective action      6.1.12
Effective parameters      6.1.22
Elliptic operator      5.6.2
Epimorphism      1.7.5
Equivalent structure constants      7.7.5
Equivalent structures      7.7.3
Euler — Poincare formula      1.4.9
Evaluation      3.1.8
Exact sequence of fibered manifolds      1.7.1
Exact sequence of vector bundles      1.4.4
Exterior derivative      5.7.1
Exterior form      1.1.23
Exterior multiplication      6.4.3
Fiber      1.1.3
Fibered chart      1.1.2
Fibered manifold      1.1.1
Fibered morphism      1.2.1
Fibered product      1.5.1
Fibered submanifold      1.3.1
Finite equivalence problem      7.5.1
Finite length sequence      1.4.8
Finite lie equations      7.1.3
Finite transformation      6.1.21
Finite type operator      5.1.15
Finite type symbol      5.1.14
Finite type system      5.1.15
First Lie theorem      6.2.1
First Spencer sequence      5.3.4
Flat pseudogroup      7.5.7
Formal derivative      2.1.5
Formal exactness      5.2.11
Formal integrability      2.3.2
Formal solution      2.3.2
Formally integrable cocycle      7.7.18
Formally transitive finite Lie equations      7.1.8
Formally transitive infinitesimal Lie equations      7.1.32
Frobenius theorem      6.3.14
Fundamental set      6.3.25
General lie equations      7.2.22
General relativity      7.2.23
Generating function      7.Pb
Graph      1.1.12
Group axioms      6.1.1
Homeomorphism      6.1.8
Homomorphism of vector bundles      1.4.1
Identity element      6.1.1
Independent vectors      6.1.23
Infinite Lie algebra      9.1.6
Infinitesimal equivalence problem      7.5.5
Infinitesimal generators      6.2.15
Infinitesimal Lie equations      7.1.29
Infinitesimal transformation      6.1.21
Inner derivation      7.8.28
Integrability conditions      7.3.10
Integrable cocycle      7.7.18
Integral element      5.6.12
Integral manifold      6.3.10
Interior multiplication      6.4.8
Invariant action      6.3.46
Invariant distribution      6.3.42
Invariant function      6.3.18
Invariant submanifold      6.3.36
Inverse      6.1.1
Involutive distribution      6.3.9

Involutive symbol      3.1.11
Involutive system      2.4.10
Isotropy subgroup      6.1.14
Jacobi conditions      7.4.8
Jacobi relations      6.2.18
Jacobian      7.1.7
jet      1.9.2
Jet bundle      1.9.4
Kernel      1.3.4
Label transformation      7.6.6
Lewry counterexample      5.7.2
Lie derivative      7.8.2
Lie form      7.1.45
Lie group      6.1.15
Lie operator      7.1.34
Lie pseudogroup      7.1.2
Linear operator      2.1.20
Linear system      5.1.2
Linearisation process      7.1.28
Local exactness      5.2.12
Local parameters      6.1.20
Local section      1.1.6
Maurer — Cartan equations      6.2.19
Maurer — Cartan forms      6.2.8
Maximum prolongation      9.1.3
Model bundle      1.1.30
Monomorphism      1.7.4
Multiplicative variable      3.2.11
Noetherian module      2.5.11
Non-linear operator      2.1.1
Non-linear system      2.2.1
Non-multiplicative variable      3.2.11
Normal bundle      1.8.1
Normal subgroup      6.1.4
normalizer      7.6.12
Obstruction      7.7.20
Ordinary bracket      6.2.10
Overdetermined system      5.6.6
P-sequence      5.5.1
Passivity      2.4.11
Permutation group      6.1.5
Poincare sequence      5.7.1
Preserving automorphism      5.2.7
Prime ideal      5.6.12
Prolongation of a morphism      2.1.3
Prolongation of a symbol      3.1.1
Prolongation of a system      2.2.3
Prolongation of a transformation      6.5.2
Prolongation of a vector space      9.1.2
Prolongation theorem      3.4.1
Proper subgroup      6.1.2
Rank      6.3.1
Reciprocal group      7.6.5
Reciprocal image      1.5.2
Regular coordinates      3.2.6
Regular map      1.2.3
Regular operator      2.1.7
Regular system      2.2.5
Related vectors      6.2.11
Restricted action      6.3.39
Rigid structure      7.7.8
Second Lie theorem      6.2.16
Second Spencer sequence      5.4.2
Short exact sequence      1.4.6
Simple group      6.1.4
Simply transitive action      6.2.5
Solution      2.2.2
Solved equation      3.2.10
Solved form      3.2.13
Source      1.9.2
Source projection      1.9.6
Special Lie equations      7.2.22
Special relativity      7.2.23
Spencer cohomology      3.1.9
Spencer family      4.1.1
Spencer operator      2.1.21
Stable Spencer sequence      5.3.5
Stationary functions      6.3.27
Stationary group      6.3.27
Structure      7.7.1
Structure constants      7.3.9
Sufficiently regular      2.5.2
Symbol of a morphism      2.1.19
Symbol of a system      2.2.6
Symbol of a vector space      9.1.1
Symbol sequence      5.6.14
Systatic covector      5.6.13
Systatic variety      5.6.13
Tangent bundle      1.1.21
TARGET      1.9.2
Target projection      1.9.6
Test board      3.2.12
Test of involutiveness      3.2.25
Theorem of analytic realization      9.1.8
Third Fundamental Theorem      7.4.12
Third Lie theorem      6.2.19
Topological group      6.1.6
Total manifold      1.1.3
Transformation group      6.1.9
Transition functions      1.1.2
Transitive action      6.1.12
Transitive vector space      9.1.4
Trivial bundle      1.1.12
Trivial deformation      7.7.7
Truncated sequence      5.5.2
Unconnected functions      6.3.22
Unconnected vectors      6.1.24
Under-determined system      5.6.6
Usual derivative      2.1.5
Vector bundle      1.1.26
Vector field      1.1.23
Vertical bundle      1.6.1
Zero theorem of Hilbert      5.6.11

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