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Springer T.A. — Linear Algebraic Groups

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Название: Linear Algebraic Groups

Автор: Springer T.A.

Аннотация:

The structure and classification of reductive groups over arbitrary fields has become a standard part of mathematics, with broad connections to many aspects of group theory (Lie groups), number theory (Langlands program, arithmetic groups), algebraic geometry and invariant theory. The first ten chapters of this text cover the theory of linear algebraic groups over algebraically closed fields, culminating in the theory of reductive groups, and includes the uniqueness and existence theorems. Chapters 11-17 cover the theory of linear algebraic groups which are not algebraically closed. The last seven chapters deal with the Tits classification of simple groups. The work is concise and self-contained, and should appeal to a broad audience of graduate students and researchers in the field. It is suitable for use as a textbook for a course on the theory, and contains exercises.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second edition

Год издания: 1998

Количество страниц: 334

Добавлена в каталог: 26.10.2010

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Предметный указатель

-form      196
-form of an -group      219
-group      21 208
-isogeny      215
-morphism      9 14
-rank      256
-rational points      6 14
-split solvable group      218
-structure      6 13 185
-subspace      185
-variety      13
-module      28
-morphism      28
-space      28
-variety      28
— Lie algebra      70
-connection      188
$\alpha$ -string      155
$\Gamma$ -module      224
$\mathbf{A}^{m, n}$       243
$\mathbf{A}^{n}$       7
$\mathbf{D}_{n}$       23
$\mathbf{GL}_{n}$       23
$\mathbf{G}_{a}$       22
$\mathbf{G}_{n}$       23
$\mathbf{M}_{n}$       23
$\mathbf{O}_{n}$       23
$\mathbf{P}^{n}$       14
$\mathbf{SL}_{n}$       23
$\mathbf{SO}_{n}$       23
$\mathbf{Sp}_{2n}$       23
$\mathbf{T}_{n}$       23
$\mathbf{U}_{n}$       23
Abelian variety      100
Additive function      49
Additive group      22
Adjacent Âorel groups      138
Adjoint semi-simple group      136
Affine -algebra      192
Affine -variety      9
Affine algebra      4
Affine algebraic variety      7
Albert algebra      306
Algebraic group      21
Algebraic variety      12
Anisotropic -group      271
Anisotropic element      282
Antipode      21
Associated fibre bundle      95
Based root datum      271
Basis of a root system      139
Big cell      149
Birational morphism      78
Borel subgroup      102
Borel’s fixed point theorem      102
Brauer group      218
Bruhat cell      149
Bruhat decomposition      145
Bruhat order      153
Bruhat’s lemma      145 270
Cartan subgroup      108
Central isogeny      171
Central simple algebra      218
CHARACTER      43
Character group      39
Closed subgroup      21
Cocenter      136
Cocharacter      43
Complete variety      98
Comultiplication      21
Connection      187
Coroots      125
Cotangent space      67
Curve      99
Defined over F      14
Deligne — Lusztig variety      153
Derivation      57
Derivation of a Lie algebra      179
Diagonalizable group      43
Differential of a homomorphism of lin ear algebraic groups      72
Differential of a morphism      58
DIMENSION      16
Direct product of algebraic groups      21
Discriminant      295
Dominant morphism      67
Dual root datum      124
Dynkin diagram      168
Elementary unipotent group      51
Equivariant line bundle      150
Equivariant morphism      28
Finite algebra      82
Finite morphism      83
Flag variety      149
Flat connection      188
Folding      182
Frobenius morphism      75 172 215
Fundamental group      136
Fundamental weights      142
Galois cohomology      216
General linear group      23
Ground field      14
Group scheme      24
Homogeneous space      28
Homomorphism of algebraic groups      21
Identity component      25
Indexed root datum      271
Indivisible roots      260
Inner form      219
Inner type      285
Involution of the first kind      290
Involution of the second kind      287
Irreducibility      2
Irreducible components      3
Irreducible root system      136
Isogeny      170 215
Isogeny Theorem      172
Isomorphism theorem      171
Isotropy group      28

Jordan decomposition in a Lie algebra      76
Jordan decomposition in a linear algebraic group      34
Jordan decomposition of an endomorphism      32
Kernel      272
Lang’s theorem      76
Length of a Weyl group dement      142
Levi subgroup      148
Lie algebra of a linear algebraic group      71
Linear algebraic group      21
Local sections      95
localization      7
Locally closed      19
Locally finite endomorphism      34
Locally finite morphism      83
Locally nilpotent endomorphism      34
Long root      168
Maximal torus      106 108
Module of differentials      60
Morphism      9
Multiplicative group      23
Nilpotent endomorphism      31
Nilpotent part of an element of a Lie algebra      77
Nilpotent part of an endomorphism      33
Non-singular variety      59
Normal integral domain      85
Normal variety      85
Octonion algebra      300
Orbit      28
Orthogonal group      23
Orthogonal involution      291
Outer form      219
Outer type      285
Parabolic subgroup      101
Principal homogeneous space      28
Principal open subset      5
Product variety      10
Projective variety      15
Pseudo-parabolic subgroup      252
Quasi-affine variety      95
Quasi-projective variety      15
Quasi-simple group      136
Quasi-split -group      271
Quotient field      16
Quotient of a linear algebraic group      93 213
Radical      112
Rank      117
Rank of a root system      155
Rational character      43
Rational closure      134
Rational representation      28
Realization      133
Reduced decomposition      142
Reduced ring      4
Reduced root system      125
Reducible root system      136
Reductive group      112
Regular function      6
Relative root system      257
Relative Weyl group      257
Restricted Lie algebra      70
Restriction of the ground field      198
Root datum      124
Root lattice      136
Root system      124
Schubert variety      149
Section      95 242
Semi-simple endomorphism      31
Semi-simple group      112
Semi-simple part of an element of a Lie algebra      77
Semi-simple part of an element of a linear algebraic group      34
Semi-simple part of an endomorphism      33
Semi-simple rank      117
Separable degree      78
Separable extension      64
Separable morphism      67
Separably algebraic      63
Separably generated extension      63
Short root      168
Simple point      59
Simple reflections      139
Simple roots      139
Simply connected semi-simple group      136
Simply laced root system      175 177
Smooth variety      59
Special linear group      23
Special orthogonal group      23
Spin group      177
Split reductive -group      271
Standard pseudo-parabolic subgroups      264
Structure constants      156
Symplectic group      23
Symplectic involution      291
System of positive roots      125
Tangent map      58 59
Tangent space      58 59
Tannaka’s theorem      37
Theorem of Kostant — Rosenlicht      36
Theorem of Lie — Kolchin      104
Torsor      28
Torus      43
Transporter      209 227
Trigonalizable      237
Twisted composition algebra      317
Twisted composition structure      316
Twisting      197
Unipotent endomorphism      31
Unipotent group      36
Unipotent part of an element of a linear algebraic group      34
Unipotent radical      112
Variety of Borel subgroups      112
Vector group      51
Weight      114
Weight lattice      136
Weight space      114
Weyl group      115
Weyl group of a root datum      124
Zariski topology      1
Zariski’s main theorem      85

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