HOME > Detail View

Detail View

Lie algebras and algebraic groups

Lie algebras and algebraic groups (Loan 8 times)

Material type
단행본
Personal Author
Tauvel, Patrice. Yu, Rupert W. T.
Title Statement
Lie algebras and algebraic groups / Patrice Tauvel, Rupert W.T. Yu.
Publication, Distribution, etc
Berlin :   Springer ,   2005.  
Physical Medium
xvi, 653 p. : ill. ; 24 cm.
Series Statement
Springer monographs in mathematics , 1439-7382
ISBN
3540241701 (hd.bd.)
Bibliography, Etc. Note
Includes bibliographical references and index.
Subject Added Entry-Topical Term
Lie algebras. Lie groups.
000 01156camuu2200337ii 4500
001 000045210960
005 20051208095225
008 051207s2005 gw a b 001 0 eng d
016 7 ▼a 973670207 ▼2 GyFmDB
020 ▼a 3540241701 (hd.bd.)
029 0 ▼a OHX ▼b har050024003
040 ▼a OHX ▼c OHX ▼d BAKER ▼d TEF ▼d IXA ▼d MBB ▼d 211009
049 ▼a KUBA
050 0 0 ▼a QA252.3 ▼b .T38 2005
072 7 ▼a QA ▼2 lcco
082 0 4 ▼a 512.55 ▼2 22
090 ▼a 512.55 ▼b T229L
100 1 ▼a Tauvel, Patrice.
245 1 0 ▼a Lie algebras and algebraic groups / ▼c Patrice Tauvel, Rupert W.T. Yu.
260 ▼a Berlin : ▼b Springer , ▼c 2005.
300 ▼a xvi, 653 p. : ▼b ill. ; ▼c 24 cm.
440 0 ▼a Springer monographs in mathematics , ▼x 1439-7382
504 ▼a Includes bibliographical references and index.
650 0 ▼a Lie algebras.
650 0 ▼a Lie groups.
700 1 ▼a Yu, Rupert W. T.
938 ▼a Otto Harrassowitz ▼b HARR ▼n har050024003 ▼c 74.85 EUR
938 ▼a Baker & Taylor ▼b BKTY ▼c 89.95 ▼d 89.95 ▼i 3540241701 ▼n 0006297277 ▼s active
945 ▼a KINS
994 ▼a C0 ▼b KUB

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.55 T229L Accession No. 121118089 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

1 Results on topological spaces 1
1.1 Irreducible sets and spaces 1
1.2 Dimension 4
1.3 Noetherian spaces 5
1.4 Constructible sets 6
1.5 Gluing topological spaces 8
2 Rings and modules 11
2.1 Ideals 11
2.2 Prime and maximal ideals 12
2.3 Rings of fractions and localization 13
2.4 Localizations of modules 17
2.5 Radical of an ideal 18
2.6 Local rings 19
2.7 Noetherian rings and modules 21
2.8 Derivations 24(1)
2.9 Module of differentials 25
3 Integral extensions 31
3.1 Integral dependence 31
3.2 Integrally closed domains 33
3.3 Extensions of prime ideals 35
4 Factorial rings 39
4.1 Generalities 39
4.2 Unique factorization 41
4.3 Principal ideal domains and Euclidean domains 43
4.4 Polynomials and factorial rings 45
4.5 Symmetric polynomials 48
4.6 Resultant and discriminant 50
5 Field extensions 55
5.1 Extensions 55
5.2 Algebraic and transcendental elements 56
5.3 Algebraic extensions 56
5.4 Transcendence basis 58
5.5 Norm and trace 60
5.6 Theorem of the primitive element 62
5.7 Going Down Theorem 64
5.8 Fields and derivations 67
5.9 Conductor 70
6 Finitely generated algebras 75
6.1 Dimension 75
6.2 Noether's Normalization Theorem 76
6.3 Krull's Principal Ideal Theorem 81
6.4 Maximal ideals 82
6.5 Zariski topology 84
7 Gradings and filtrations 87
7.1 Graded rings and graded modules 87
7.2 Graded submodules 88
7.3 Applications 90
7.4 Filtrations 91
7.5 Grading associated to a filtration 92
8 Inductive limits 95
8.1 Generalities 95
8.2 Inductive systems of maps 96
8.3 Inductive systems of magmas, groups and rings 98
8.4 An example 100
8.5 Inductive systems of algebras 100
9 Sheaves of functions 103
9.1 Sheaves 103
9.2 Morphisms 104
9.3 Sheaf associated to a presheaf 106
9.4 Gluing 109(1)
9.5 Ringed space 110
10 Jordan decomposition and some basic results on groups 113
10.1 Jordan decomposition 113
10.2 Generalities on groups 117
10.3 Commutators 118
10.4 Solvable groups 120
10.5 Nilpotent groups 121
10.6 Group actions 122
10.7 Generalities on representations 123
10.8 Examples 126
11 Algebraic sets 131
11.1 Affine algebraic sets 131
11.2 Zariski topology 132
11.3 Regular functions 133
11.4 Morphisms 134
11.5 Examples of morphisms 136
11.6 Abstract algebraic sets 138
11.7 Principal open subsets 140
11.8 Products of algebraic sets 142
12 Prevarieties and varieties 147
12.1 Structure sheaf 147
12.2 Algebraic prevarieties 149
12.3 Morphisms of prevarieties 151
12.4 Products of prevarieties 152
12.5 Algebraic varieties 155
12.6 Gluing 158
12.7 Rational functions 159
12.8 Local rings of a variety 162
13 Projective varieties 167
13.1 Projective spaces 167
13.2 Projective spaces and varieties 168
13.3 Cones and projective varieties 171
13.4 Complete varieties 176
13.5 Products 178
13.6 Grassmannian variety 180
14 Dimension 183
14.1 Dimension of varieties 183
14.2 Dimension and the number of equations 185
14.3 System of parameters 187
14.4 Counterexamples 190
15 Morphisms and dimension 191
15.1 Criterion of affineness 191
15.2 Affine morphisms 193
15.3 Finite morphisms 194
15.4 Factorization and applications 197
15.5 Dimension of fibres of a morphism 199
15.6 An example 203
16 Tangent spaces 205
16.1 A first approach 205
16.2 Zariski tangent space 207
16.3 Differential of a morphism 209
16.4 Some lemmas 213
16.5 Smooth points 215
17 Normal varieties 219
17.1 Normal varieties 219
17.2 Normalization 221
17.3 Products of normal varieties 223
17.4 Properties of normal varieties 225
18 Root systems 233
18.1 Reflections 233
18.2 Root systems 235
18.3 Root systems and bilinear forms 238
18.4 Passage to the field of real numbers 239
18.5 Relations between two roots 240
18.6 Examples of root systems 243
18.7 Base of a root system 244
18.8 Weyl chambers 247
18.9 Highest root 250
18.10 Closed subsets of roots 250
18.11 Weights 253
18.12 Graphs 255
18.13 Dynkin diagrams 256
18.14 Classification of root systems 259
19 Lie algebras 277
19.1 Generalities on Lie algebras 277
19.2 Representations 279
19.3 Nilpotent Lie algebras 282
19.4 Solvable Lie algebras 286
19.5 Radical and the largest nilpotent ideal 289
19.6 Nilpotent radical 291
19.7 Regular linear forms 292
19.8 Cartan subalgebras 294
20 Semisimple and reductive Lie algebras 299
20.1 Semisimple Lie algebras 299
20.2 Examples 301
20.3 Semisimplicity of representations 302
20.4 Semisimple and nilpotent elements 305
20.5 Reductive Lie algebras 307
20.6 Results on the structure of semisimple Lie algebras 310
20.7 Subalgebras of semisimple Lie algebras 313
20.8 Parabolic subalgebras 316
21 Algebraic groups 319
21.1 Generalities 319
21.2 Subgroups and morphisms 321
21.3 Connectedness 322
21.4 Actions of an algebraic group 325
21.5 Modules 326
21.6 Group closure 327
22 Affine algebraic groups 331
22.1 Translations of functions 331
22.2 Jordan decomposition 333
22.3 Unipotent groups 335
22.4 Characters and weights 338
22.5 Tori and diagonalizable groups 340
22.6 Groups of dimension one 345
23 Lie algebra of an algebraic group 347
23.1 An associative algebra 347
23.2 Lie algebras 348
23.3 Examples 352
23.4 Computing differentials 354
23.5 Adjoint representation 359
23.6 Jordan decomposition 362
24 Correspondence between groups and Lie algebras 365
24.1 Notations 365
24.2 An algebraic subgroup 365
24.3 Invariants 368
24.4 Functorial properties 372
24.5 Algebraic Lie subalgebras 375
24.6 A particular case 380
24.7 Examples 383
24.8 Algebraic adjoint group 383
25 Homogeneous spaces and quotients 387
25.1 Homogeneous spaces 387
25.2 Some remarks 389
25.3 Geometric quotients 391
25.4 Quotient by a subgroup 393
25.5 The case of finite groups 397
26 Solvable groups 401
26.1 Conjugacy classes 401
26.2 Actions of diagonalizable groups 405
26.3 Fixed points 406
26.4 Properties of solvable groups 407
26.5 Structure of solvable groups 409
27 Reductive groups 413
27.1 Radical and unipotent radical 413
27.2 Semisimple and reductive groups 415
27.3 Representations 416
27.4 Finiteness properties 420
27.5 Algebraic quotients 422
27.6 Characters 424
28 Borel subgroups, parabolic subgroups, Cartan subgroups 429
28.1 Borel subgroups 429
28.2 Theorems of density 432
28.3 Centralizers and tori 434
28.4 Properties of parabolic subgroups 435
28.5 Cartan subgroups 437
29 Cartan subalgebras, Borel subalgebras and parabolic subalgebras 441
29.1 Generalities 441(2)
29.2 Cartan subalgebras 443
29.3 Applications to semisimple Lie algebras 446
29.4 Borel subalgebras 447
29.5 Properties of parabolic subalgebras 450
29.6 More on reductive Lie algebras 453
29.7 Other applications 454
29.8 Maximal subalgebras 45
30 Representations of semisimple Lie algebras 459
30.1 Enveloping algebra 459
30.2 Weights and primitive elements 461
30.3 Finite-dimensional modules 463
30.4 Verma modules 464
30.5 Results on existence and uniqueness 467
30.6 A property of the Weyl group 469
31 Symmetric invariants 471
31.1 Invariants of finite groups 471
31.2 Invariant polynomial functions 475
31.3 A free module 478
32 S-triples 481
32.1 Jacobson-Morosov Theorem 481
32.2 Some lemmas 484
32.3 Conjugation of S-triples 487
32.4 Characteristic 488
32.5 Regular and principal elements 489
33 Polarizations 493
33.1 Definition of polarizations 493
33.2 Polarizations in the semisimple case 494
33.3 A non-polarizable element 497
33.4 Polarizable elements 499
33.5 Richardson's Theorem 502
34 Results on orbits 507
34.1 Notations 507
34.2 Some lemmas 508
34.3 Generalities on orbits 509
34.4 Minimal nilpotent orbit 511
34.5 Subregular nilpotent orbit 513
34.6 Dimension of nilpotent orbits 517
34.7 Prehomogeneous spaces of parabolic type 518
35 Centralizers 521
35.1 Distinguished elements 521
35.2 Distinguished parabolic subalgebras 523
35.3 Double centralizers 525
35.4 Normalizers 528
35.5 A semisimple Lie subalgebra 530
35.6 Centralizers and regular elements 533
36 σ-root systems 537
36.1 Definition 537
36.2 Restricted root systems 539
36.3 Restriction of a root 544
37 Symmetric Lie algebras 549
37.1 Primary subspaces 549
37.2 Definition of symmetric Lie algebras 553
37.3 Natural subalgebras 554
37.4 Cartan subspaces 555
37.5 The case of reductive Lie algebras 557
37.6 Linear forms 559
38 Semisimple symmetric Lie algebras 561
38.1 Notations 561
38.2 Iwasawa decomposition 562
38.3 Coroots 565
38.4 Centralizers 568
38.5 S-triples 570
38.6 Orbits 573
38.7 Symmetric invariants 579
38.8 Double centralizers 584
38.9 Normalizers 588
38.10 Distinguished elements 589
39 Sheets of Lie algebras 593
39.1 Jordan classes 593
39.2 Topology of Jordan classes 596
39.3 Sheets 601
39.4 Dixmier sheets 603
39.5 Jordan classes in the symmetric case 605
39.6 Sheets in the symmetric case 608
40 Index and linear forms 611
40.1 Stable linear forms 611
40.2 Index of a representation 615
40.3 Some useful inequalities 616
40.4 Index and semi-direct products 618
40.5 Heisenberg algebras in semisimple Lie algebras 621
40.6 Index of Lie subalgebras of Borel subalgebras 625
40.7 Seaweed Lie algebras 629
40.8 An upper bound for the index 630
40.9 Cases where the bound is exact 635
40.10 On the index of parabolic subalgebras 638
References 641
List of notations 645
Index 647


Information Provided By: : Aladin

New Arrivals Books in Related Fields