Actions and invariants of algebraic groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2005
|
| Series: | Pure and applied mathematics
269 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 454 S. graph. Darst. |
| ISBN: | 9780824758967 082475896X |
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Record in the Search Index
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| adam_text | ACTIONS AND INVARIANTS OF ALGEBRAIC GROUPS WALTER FERRER SANTOS
UNIVERSIDAD DE LA REPUBLICA MONTEVIDEO, URUGUAY ALVARO RITTATORE
UNIVERSIDAD DE LA REPUBLICA MONTEVIDEO, URUGUAY CHAPMAN & A HALL/CRC
TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK SINGAPORE CONTENTS
PREFACE XI ENUMERATION OF ITEMS AND CROSS REFERENCES XV CHAPTER 1.
ALGEBRAIC GEOMETRY 1 1. INTRODUCTION 1 2. COMMUTATIVE ALGEBRA 3 2.1.
RING AND FIELD EXTENSIONS 3 2.2. HILBERT S NULLSTELLENSATZ 7 2.3.
SEPARABILITY 9 2.4. FAITHFULLY FLAT RING EXTENSIONS 12 2.5. REGULAR
LOCAL RINGS 13 3. ALGEBRAIC SUBSETS OF THE AFFINE SPACE 14 3.1. BASIC
DEFINITIONS 14 3.2. THE ZARISKI TOPOLOGY 17 3.3. POLYNOMIAL MAPS.
MORPHISMS 19 4. ALGEBRAIC VARIETIES 23 4.1. SHEAVES ON TOPOLOGICAL
SPACES 23 4.2. THE MAXIMAL SPECTRUM 26 4.3. AFFINE ALGEBRAIC VARIETIES
27 4.4. ALGEBRAIC VARIETIES 34 4.5. MORPHISMS OF ALGEBRAIC VARIETIES 45
4.6. COMPLETE VARIETIES 51 4.7. SINGULAR POINTS AND NORMAL VARIETIES 53
5. DEEPER RESULTS ON MORPHISMS 56 6. EXERCISES 64 CHAPTER 2. LIE
ALGEBRAS 73 1. INTRODUCTION 73 2. DEFINITIONS AND BASIC CONCEPTS 74 3.
THE THEOREMS OF F. ENGEL AND S. LIE * 78 4. SEMISIMPLE LIE ALGEBRAS 84
5. COHOMOLOGY OF LIE ALGEBRAS 89 6. THE THEOREMS OF H. WEYL AND F. LEVI
97 7. P-LIE ALGEBRAS 99 8. EXERCISES 101 CHAPTER 3. ALGEBRAIC GROUPS:
BASIC DEFINITIONS 107 1. INTRODUCTION 107 2. DEFINITIONS AND BASIC
CONCEPTS 108 3. SUBGROUPS AND HOMOMORPHISRNS 114 4. ACTIONS OF AFFINE
GROUPS ON ALGEBRAIC VARIETIES 116 5. SUBGROUPS AND SEMIDIRECT PRODUCTS
121 6. EXERCISES 126 CHAPTER 4. ALGEBRAIC GROUPS: LIE ALGEBRAS AND
REPRESENTATIONS 131 1. INTRODUCTION 131 2. HOPF ALGEBRAS AND ALGEBRAIC
GROUPS 132 3. RATIONAL G-MODULES 139 4. REPRESENTATIONS OF SL 2 149 5.
CHARACTERS AND SEMI-INVARIANTS 151 6. THE LIE ALGEBRA ASSOCIATED TO AN
AFFINE ALGEBRAIC GROUP 154 7. EXPLICIT COMPUTATIONS 157 8. EXERCISES 165
CHAPTER 5. ALGEBRAIC GROUPS: JORDAN DECOMPOSITION AND APPLICATIONS 173
1. INTRODUCTION 173 2. THE JORDAN DECOMPOSITION OF A SINGLE OPERATOR 174
3. THE JORDAN DECOMPOSITION OF AN ALGEBRA HOMOMORPHISM AND OF A
DERIVATION 179 4. JORDAN DECOMPOSITION FOR COALGEBRAS 181 5. JORDAN
DECOMPOSITION FOR AN AFFINE ALGEBRAIC GROUP 187 6. UNIPOTENCY AND
SEMISIMPLICITY 191 7. THE SOLVABLE AND THE UNIPOTENT RADICAL 198 8.
STRUCTURE OF SOLVABLE GROUPS 204 9. THE CLASSICAL GROUPS 210 9.1. THE
GENERAL LINEAR GROUP GL N 210 9.2. THE SPECIAL LINEAR GROUP SL N (CASE
A) 211 9.3. THE PROJECTIVE GENERAL LINEAR GROUP PGL N (K) (CASE A) 212
9.4. THE SPECIAL ORTHOGONAL GROUP SO N (CASES B,D) 213 9.5. THE
SYMPLECTIC GROUP SP N , N = 2M (CASE C) 214 10. EXERCISES 215 CHAPTER 6.
ACTIONS OF ALGEBRAIC GROUPS 219 1. INTRODUCTION 219 2. ACTIONS: EXAMPLES
AND FIRST PROPERTIES 220 3. BASIC FACTS ABOUT THE GEOMETRY OF THE ORBITS
224 4. CATEGORICAL AND GEOMETRIC QUOTIENTS 227 5. THE SUBALGEBRA OF
INVARIANTS 238 6. INDUCTION AND RESTRICTION OF REPRESENTATIONS 242 7.
EXERCISES 248 CHAPTER 7. HOMOGENEOUS SPACES 253 1. INTRODUCTION 253 2.
EMBEDDING FF-MODULES INSIDE G-MODULES 254 3. DEFINITION OF SUBGROUPS IN
TERMS OF SEMI-INVARIANTS 258 4. THE COSET SPACE G/H AS A GEOMETRIC
QUOTIENT 266 5. QUOTIENTS BY NORMAL SUBGROUPS 268 6. APPLICATIONS AND
EXAMPLES 271 7. EXERCISES 276 CHAPTER 8. ALGEBRAIC GROUPS AND LIE
ALGEBRAS IN CHARACTERISTIC ZERO 279 1. INTRODUCTION 279 2.
CORRESPONDENCE BETWEEN SUBGROUPS AND SUBALGEBRAS 281 3. ALGEBRAIC LIE
ALGEBRAS 287 4. EXERCISES 291 CHAPTER 9. REDUCTIVITY 295 1. INTRODUCTION
295 2. LINEAR AND GEOMETRIC REDUCTIVITY 297 3. EXAMPLES OF LINEARLY AND
GEOMETRICALLY REDUCTIVE GROUPS 308 4. REDUCTIVITY AND THE STRUCTURE OF
THE GROUP 314 5. REDUCTIVE GROUPS ARE LINEARLY REDUCTIVE IN
CHARACTERISTIC ZERO 318 6. EXERCISES 320 CHAPTER 10. OBSERVABLE
SUBGROUPS OF AFFINE ALGEBRAIC GROUPS 323 1. INTRODUCTION - 323 2. BASIC
DEFINITIONS 324 3. INDUCTION AND OBSERVABILITY 328 4. SPLIT AND STRONG
OBSERVABILITY 330 5. THE, GEOMETRIC CHARACTERIZATION OF OBSERVABILITY
339 6. EXERCISES 341 CHAPTER 11. AFFINE HOMOGENEOUS SPACES 345 1.
INTRODUCTION 345 2. GEOMETRIC REDUCTIVITY AND OBSERVABILITY 346 3. EXACT
SUBGROUPS 347 4. FROM QUASI-AFFINE TO AFFINE HOMOGENEOUS SPACES 348 5.
EXACTNESS, REYNOLDS OPERATORS, TOTAL INTEGRALS 350 6. AFFINE HOMOGENEOUS
SPACES AND EXACTNESS 353 7. AFFINE HOMOGENEOUS SPACES AND REDUCTIVITY
356 8. EXACTNESS AND INTEGRALS FOR UNIPOTENT GROUPS 357 9. EXERCISES 360
CHAPTER 12. HILBERT S 14 TH PROBLEM 363 1. INTRODUCTION 363 2. A
COUNTEREXAMPLE TO HILBERT S 14 TH PROBLEM 366 3. REDUCTIVE GROUPS AND
FINITE GENERATION OF INVARIANTS 375 4. V. POPOV S CONVERSE TO NAGATA S
THEOREM 379 5. PARTIAL POSITIVE ANSWERS TO HILBERT S 14 TH PROBLEM 381
6. GEOMETRIC CHARACTERIZATION OF GROSSHANS PAIRS 387 7. EXERCISES 389
CHAPTER 13. QUOTIENTS 393 1. INTRODUCTION 393 2. ACTIONS BY REDUCTIVE
GROUPS: THE CATEGORICAL QUOTIENT 394 3. ACTIONS BY REDUCTIVE GROUPS: THE
GEOMETRIC QUOTIENT 400 4. CANONICAL FORMS OF MATRICES: A GEOMETRIC
PERSPECTIVE 404 5. ROSENLICHT S THEOREM 407 6. FURTHER RESULTS ON
INVARIANTS OF FINITE GROUPS 410 6.1. INVARIANTS OF GRADED ALGEBRAS 411
6.2. POLYNOMIAL SUBALGEBRAS OF POLYNOMIAL ALGEBRAS 413 6.3. THE CASE OF
A GROUP GENERATED BY REFLECTIONS 417 6.4. THE DEGREE OF THE FUNDAMENTAL
INVARIANTS FOR A FINITE GROUP 419 7. EXERCISES 420 APPENDIX. BASIC
DEFINITIONS AND RESULTS 423 1. INTRODUCTION 423 2. NOTATIONS 423 2.1.
CATEGORY THEORY 423 2.2. GENERAL TOPOLOGY 424 2.3. LINEAR ALGEBRA 424
2.4. GROUP THEORY 425 3. RINGS AND MODULES 427 4. REPRESENTATIONS 431
BIBLIOGRAPHY 433 GLOSSARY OF NOTATIONS 441 AUTHOR INDEX 445 INDEX 447
|
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| indexdate | 2024-07-09T20:06:26Z |
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| isbn | 9780824758967 082475896X |
| language | English |
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| spelling | Ferrer Santos, Walter Verfasser aut Actions and invariants of algebraic groups Walter Ferrer Santos ; Alvaro Rittatore Boca Raton [u.a.] Chapman & Hall/CRC 2005 XVI, 454 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 269 Groupes algébriques affines Grupos algébricos larpcal Invariantes (álgebra) larpcal Invariants Affine algebraic groups Algebraische Gruppe (DE-588)4001164-1 gnd rswk-swf Invariantentheorie (DE-588)4162209-1 gnd rswk-swf Affine algebraische Gruppe (DE-588)4141561-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Affine algebraische Gruppe (DE-588)4141561-9 s DE-604 Invariantentheorie (DE-588)4162209-1 s Algebraische Gruppe (DE-588)4001164-1 s Rittatore, Alvaro Verfasser aut Pure and applied mathematics 269 (DE-604)BV000001885 269 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013126924&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ferrer Santos, Walter Rittatore, Alvaro Actions and invariants of algebraic groups Pure and applied mathematics Groupes algébriques affines Grupos algébricos larpcal Invariantes (álgebra) larpcal Invariants Affine algebraic groups Algebraische Gruppe (DE-588)4001164-1 gnd Invariantentheorie (DE-588)4162209-1 gnd Affine algebraische Gruppe (DE-588)4141561-9 gnd |
| subject_GND | (DE-588)4001164-1 (DE-588)4162209-1 (DE-588)4141561-9 (DE-588)4123623-3 |
| title | Actions and invariants of algebraic groups |
| title_auth | Actions and invariants of algebraic groups |
| title_exact_search | Actions and invariants of algebraic groups |
| title_full | Actions and invariants of algebraic groups Walter Ferrer Santos ; Alvaro Rittatore |
| title_fullStr | Actions and invariants of algebraic groups Walter Ferrer Santos ; Alvaro Rittatore |
| title_full_unstemmed | Actions and invariants of algebraic groups Walter Ferrer Santos ; Alvaro Rittatore |
| title_short | Actions and invariants of algebraic groups |
| title_sort | actions and invariants of algebraic groups |
| topic | Groupes algébriques affines Grupos algébricos larpcal Invariantes (álgebra) larpcal Invariants Affine algebraic groups Algebraische Gruppe (DE-588)4001164-1 gnd Invariantentheorie (DE-588)4162209-1 gnd Affine algebraische Gruppe (DE-588)4141561-9 gnd |
| topic_facet | Groupes algébriques affines Grupos algébricos Invariantes (álgebra) Invariants Affine algebraic groups Algebraische Gruppe Invariantentheorie Affine algebraische Gruppe Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013126924&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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