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Coutinho S.C. — A primer of algebraic D-modules
Coutinho S.C. — A primer of algebraic D-modules



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Название: A primer of algebraic D-modules

Автор: Coutinho S.C.

Аннотация:

The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications, avoiding all unnecessary technicalities. The author takes an algebraic approach, concentrating on the role of the Weyl algebra. The author assumes very few prerequisites, and the book is virtually self-contained. The author includes exercises at the end of each chapter and gives the reader ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.


Язык: en

Рубрика: Математика/Алгебра/Дифференциальная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 207

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathcal C^\infty$-function      42 45
Abelian category      166
Algebraic analysis      4
Algebraic function      41
Artin — Schreier theorem      89
Artinian module      88
Artinian ring      89
Ascending chain condition      66
Associated graded algebra      57
Associated graded module      60
Asympototic stability      171
Asymptotically stable point      171
Automorphisms of $A_n$      11
Balanced map      111
Bernstein filtration      56
Bernstein inequality      83
Bernstein polynomial      94
Bilinear map      111
Bimodule      108
Canonical basis      9
Canonical form      9
Category      166
Change of rings      130
Characteristic ideal      98
Characteristic variety      98
Closed ideal      102
Co-isotropic subspace      101
Commutator      9
Comorphism      27
Complex neighbourhood      51
Composition of direct images      165
Composition of inverse images      140
Composition series      89
D-module      3
D-module of differential equation      44
Degree of operator      14
Derivation      20
Difference function      74
Dimension of $A_n$-module      77
Dimension of Gelfand — Kirillov      80
Dimension of variety      99
Dirac's $\delta$      46
Dirac's $\delta$ as hyperfunction      51
Dirac's $\delta$ as microfunction      49
Direct image as functor      167
Direct image of left modules      151
Direct image of right modules      146
Direct image under embeddings      154
Direct image under isomorphisms      152
Direct image under projections      151
Direct limit      47
Directed family      46
Directed set      46
Distributions      44
Dixmier conjecture      34
Dynamical variables      2
Endomorphisms of $A_n$      16
Enveloping algebra      3
External product of algebras      121
External product of modules      122
Factorial of multi-index      10
Filtered algebra      56
Filtered module      59
Filtration of algebra      56
Filtration of module      59
Fourier series      2
Fourier transform      39
functor      166
Fundamental theorem of calculus      184
Gelfand — Kirillov dimension      80
Generically defined property      106
Germs of holomorphic functions      47
Global asymptotic stability      172
Globally asymptotically stable point      172
Good filtration      70
Gosper's algorithm      186
Graded algebra      53 57
Graded homomorphism      54 55
Graded ideal      54
Graded module      55
Graded submodule      55
Grading      53
Green's theorem      176 178
Heaviside hyperfunction      51
Heaviside microfunction      50
Hilbert basis theorem      68
Hilbert polynomial      74
Holomorphic function      40
Holonomic function      179
Holonomic module      86
Homogeneous component      53
Homogeneous element      53
Hyperexponential functions      180
Hyperfunctions      44 51
Hypergeometric function      4
Hypergeometric sequences      180
Induced filtration      61
Inverse function theorem      28
Inverse image      132
Inverse image as functor      166
Inverse image of $A_n$-modules      132
Inverse image of Dirac's $\delta$      137
Inverse image over polynomial rings      132
Inverse image under embeddings      138
Inverse image under isomorphisms      143
Inverse image under projections      134
Involutive subspace      101
Involutive variety      101
Irreducible module      36
Isotropic subspace      101
Jacobian conjecture      28 33
Jacobian conjecture, for comorphisms      30
Jacobian conjecture, in dimension 1      28
Jacobian conjecture, in positive characteristic      35
Jacobian determinant      28
Jacobian matrix      28
Kashiwara's theorem      158 168
Lagrangian varieties      102
Length of composition series      89
Length of multi-index      9
Lie algebra      3
Local inversion theorem      33 194
localization      119 186
Locally nilpotent derivation      30
Matrix mechanics      2
Maximal condition      66
Maximal element      66
Metrizable space      50
Microdifferential operators      189
Microfunctions      44 46 49
Minimal element      88
Minimal involutive variety      105
Module of hyperfunctions      51
Module of microfunctions      49
Module with support      159
Multi-index      9
Multiplication map      121
Multiplicity      77
Noetherian module      65
Noetherian ring      67
Non-singular point      99
Numerical polynomial      74
Oere condition      84
Order filtration      56 63
Order in $A_n$      22 56
Order in $B_n(K)$      18
Order of operator      20
Poisson bracket      102
Polynomial algebra      8
Polynomial isomorphism      26
Polynomial map      26
Polynomial ring      8 36
Polynomial solution      44
Positive grading      53
Pre-ordered set      46
Preservation of holonomy under direct image      165
Preservation of holonomy under inverse image      162 165
Principal symbol      63
Quantum algebra      2
Quantum group      53
quantum mechanics      1
Quantum plane      53
Quivers      50
Regular holonomic module      107
Resolution of singularities      4
Riemann — Hilbert correspondence      4 190
Ring of constants      30
Ring of coordinates      188
Ring of differential operators      21
Simple module      36
Simple ring      16
Singular point      99
Skew orthogonal complement      100
Skew symmetic form      100
Solution space      45
Standard embedding      138
Standard symplectic structure      100
Standard transposition      147
Structure sheaf      188
Sub-bimodule      108
Support of element      156
Support of module      159
Symbol ideal      63
Symbol map      57 60
Symplectic geometry      100
Symplectic group      64
Symplectic structure      100
Tensor product      109
Torsion element      36
Torsion module      36
Transposed action      148
Transposed bimodule      149
Transposed module      148
Transposition      147
Twisted module      38
Uniqueness theorem for differential equations      171
Universal balanced map      111
Universal cover      48
Universal property of tensor product      112
Wave mechanics      2
Weyl algebra as differential operators      8
Weyl algebra as quotient of free algebra      10
Weyl algebra in positive characteristic      17
Zariski tangent space      99
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