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Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan
Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan
Autore Borel Armand
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2002]
Descrizione fisica 1 online resource (153 p.)
Disciplina 510 s
512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Lie groups
Compact groups
Root systems (Algebra)
Soggetto genere / forma Electronic books.
ISBN 1-4704-0340-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Chapter 1. Introduction""; ""1.1. Preliminaries""; ""1.2. The case of commuting pairs in a simply connected group""; ""1.3. c-pairs""; ""1.4. Commuting triples""; ""1.5. C-triples""; ""1.6. Quotients of diagram automorphisms""; ""1.7. Description of S(k) and S[sup(Ï?c)](g,k)""; ""1.8. Chern-Simons invariants and Witten's ""Clockwise Symmetry Conjecture""""; ""1.9. Outline of the paper""; ""1.10. History""; ""Chapter 2. Almost commuting N-tuples""; ""2.1. An invariant for almost commuting N-tuples""; ""2.2. The case of rank zero""; ""2.3. The case of arbitrary rank""
""Chapter 3. Some characterizations of groups of type A""""3.1. Generalities on subroot systems""; ""3.2. Action of CG on an alcove""; ""3.3. A first characterization of groups of type A""; ""3.4. Subgroups associated with elements of the center""; ""3.5. A further characterization of products of groups of type A""; ""3.6. A consequence of Proposition 3.5.1""; ""3.7. Application to generalized Cartan matrices and affine diagrams""; ""3.8. Numerology of clockwise symmetry""; ""Chapter 4. c-pairs""; ""4.1. The rank zero case""; ""4.2. The general case""; ""Chapter 5. Commuting triples""
""5.1. Commuting triples of rank zero""""5.2. A list of all simple groups with rank zero commuting triples""; ""5.3. Action of the outer automorphism group of G""; ""5.4. Action of the center of G""; ""5.5. The general case""; ""Chapter 6. Some results on diagram automorphisms and associated root systems""; ""6.1. A chamber structure and a Coxeter group on the fixed subspace""; ""6.2. The restricted root system and the projection root system""; ""6.3. Generalized Cartan matrices for Î?[sup(res)](l) and Î?[sup(proj)](l)[sup(v)]""; ""6.4. The case of an outer automorphism""
""6.5. Further results under an additional hypothesis""""6.6. The case of a subgroup of CÎ?""; ""6.7. Proof of Theorem 1.6.2""; ""Chapter 7. The fixed subgroup of an automorphism""; ""7.1. A first description of the component group""; ""7.2. Special automorphisms""; ""7.3. A complete description of the component group""; ""7.4. The roots of H[sup(Ï?)]""; ""7.5. The case of c-pairs""; ""7.6. Variation of Ï€[sub(0)](Z(x,y)) as x varies""; ""Chapter 8. C-triples""; ""8.1. c-triples of rank zero""; ""8.2. The maximal torus of a c-triple of order k""; ""8.3. The number of components""
""10.2. Flat connections and the Chern-Simons invariant""
Record Nr. UNINA-9910480939903321
Borel Armand  
Providence, Rhode Island : , : American Mathematical Society, , [2002]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan
Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan
Autore Borel Armand
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2002]
Descrizione fisica 1 online resource (153 p.)
Disciplina 510 s
512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Lie groups
Compact groups
Root systems (Algebra)
ISBN 1-4704-0340-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Chapter 1. Introduction""; ""1.1. Preliminaries""; ""1.2. The case of commuting pairs in a simply connected group""; ""1.3. c-pairs""; ""1.4. Commuting triples""; ""1.5. C-triples""; ""1.6. Quotients of diagram automorphisms""; ""1.7. Description of S(k) and S[sup(Ï?c)](g,k)""; ""1.8. Chern-Simons invariants and Witten's ""Clockwise Symmetry Conjecture""""; ""1.9. Outline of the paper""; ""1.10. History""; ""Chapter 2. Almost commuting N-tuples""; ""2.1. An invariant for almost commuting N-tuples""; ""2.2. The case of rank zero""; ""2.3. The case of arbitrary rank""
""Chapter 3. Some characterizations of groups of type A""""3.1. Generalities on subroot systems""; ""3.2. Action of CG on an alcove""; ""3.3. A first characterization of groups of type A""; ""3.4. Subgroups associated with elements of the center""; ""3.5. A further characterization of products of groups of type A""; ""3.6. A consequence of Proposition 3.5.1""; ""3.7. Application to generalized Cartan matrices and affine diagrams""; ""3.8. Numerology of clockwise symmetry""; ""Chapter 4. c-pairs""; ""4.1. The rank zero case""; ""4.2. The general case""; ""Chapter 5. Commuting triples""
""5.1. Commuting triples of rank zero""""5.2. A list of all simple groups with rank zero commuting triples""; ""5.3. Action of the outer automorphism group of G""; ""5.4. Action of the center of G""; ""5.5. The general case""; ""Chapter 6. Some results on diagram automorphisms and associated root systems""; ""6.1. A chamber structure and a Coxeter group on the fixed subspace""; ""6.2. The restricted root system and the projection root system""; ""6.3. Generalized Cartan matrices for Î?[sup(res)](l) and Î?[sup(proj)](l)[sup(v)]""; ""6.4. The case of an outer automorphism""
""6.5. Further results under an additional hypothesis""""6.6. The case of a subgroup of CÎ?""; ""6.7. Proof of Theorem 1.6.2""; ""Chapter 7. The fixed subgroup of an automorphism""; ""7.1. A first description of the component group""; ""7.2. Special automorphisms""; ""7.3. A complete description of the component group""; ""7.4. The roots of H[sup(Ï?)]""; ""7.5. The case of c-pairs""; ""7.6. Variation of Ï€[sub(0)](Z(x,y)) as x varies""; ""Chapter 8. C-triples""; ""8.1. c-triples of rank zero""; ""8.2. The maximal torus of a c-triple of order k""; ""8.3. The number of components""
""10.2. Flat connections and the Chern-Simons invariant""
Record Nr. UNINA-9910788846203321
Borel Armand  
Providence, Rhode Island : , : American Mathematical Society, , [2002]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan
Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan
Autore Borel Armand
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2002]
Descrizione fisica 1 online resource (153 p.)
Disciplina 510 s
512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Lie groups
Compact groups
Root systems (Algebra)
ISBN 1-4704-0340-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Chapter 1. Introduction""; ""1.1. Preliminaries""; ""1.2. The case of commuting pairs in a simply connected group""; ""1.3. c-pairs""; ""1.4. Commuting triples""; ""1.5. C-triples""; ""1.6. Quotients of diagram automorphisms""; ""1.7. Description of S(k) and S[sup(Ï?c)](g,k)""; ""1.8. Chern-Simons invariants and Witten's ""Clockwise Symmetry Conjecture""""; ""1.9. Outline of the paper""; ""1.10. History""; ""Chapter 2. Almost commuting N-tuples""; ""2.1. An invariant for almost commuting N-tuples""; ""2.2. The case of rank zero""; ""2.3. The case of arbitrary rank""
""Chapter 3. Some characterizations of groups of type A""""3.1. Generalities on subroot systems""; ""3.2. Action of CG on an alcove""; ""3.3. A first characterization of groups of type A""; ""3.4. Subgroups associated with elements of the center""; ""3.5. A further characterization of products of groups of type A""; ""3.6. A consequence of Proposition 3.5.1""; ""3.7. Application to generalized Cartan matrices and affine diagrams""; ""3.8. Numerology of clockwise symmetry""; ""Chapter 4. c-pairs""; ""4.1. The rank zero case""; ""4.2. The general case""; ""Chapter 5. Commuting triples""
""5.1. Commuting triples of rank zero""""5.2. A list of all simple groups with rank zero commuting triples""; ""5.3. Action of the outer automorphism group of G""; ""5.4. Action of the center of G""; ""5.5. The general case""; ""Chapter 6. Some results on diagram automorphisms and associated root systems""; ""6.1. A chamber structure and a Coxeter group on the fixed subspace""; ""6.2. The restricted root system and the projection root system""; ""6.3. Generalized Cartan matrices for Î?[sup(res)](l) and Î?[sup(proj)](l)[sup(v)]""; ""6.4. The case of an outer automorphism""
""6.5. Further results under an additional hypothesis""""6.6. The case of a subgroup of CÎ?""; ""6.7. Proof of Theorem 1.6.2""; ""Chapter 7. The fixed subgroup of an automorphism""; ""7.1. A first description of the component group""; ""7.2. Special automorphisms""; ""7.3. A complete description of the component group""; ""7.4. The roots of H[sup(Ï?)]""; ""7.5. The case of c-pairs""; ""7.6. Variation of Ï€[sub(0)](Z(x,y)) as x varies""; ""Chapter 8. C-triples""; ""8.1. c-triples of rank zero""; ""8.2. The maximal torus of a c-triple of order k""; ""8.3. The number of components""
""10.2. Flat connections and the Chern-Simons invariant""
Record Nr. UNINA-9910812749903321
Borel Armand  
Providence, Rhode Island : , : American Mathematical Society, , [2002]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Cohomologie des espaces localement compacts d'apres J. Leray [[electronic resource] ] : Exposes faits au Seminaire de topologie algebrique de l'Ecole polytechnique federale au printemps 1951 / / by Armand Borel
Cohomologie des espaces localement compacts d'apres J. Leray [[electronic resource] ] : Exposes faits au Seminaire de topologie algebrique de l'Ecole polytechnique federale au printemps 1951 / / by Armand Borel
Autore Borel Armand
Edizione [3rd ed. 1964.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1964
Descrizione fisica 1 online resource (93p.)
Disciplina 510
Collana Lecture Notes in Mathematics
Soggetto topico Mathematics
Mathematics, general
ISBN 3-540-36803-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione fre
Nota di contenuto Notions algebriques -- Les complexes -- Le theoreme fondamental -- Applications et complements -- Les faisceauk -- L'algebre spectrale -- Algebre spectrale d'une application continue -- Algebre spectrale des espaces fibres -- Applications aux espaces fibres.
Record Nr. UNISA-996466475303316
Borel Armand  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1964
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Essays in the history of Lie groups and algebraic groups / / Armand Borel
Essays in the history of Lie groups and algebraic groups / / Armand Borel
Autore Borel Armand
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society : , : London Mathematical Society, , 2001
Descrizione fisica 1 online resource (185 pages) : illustrations, photographs
Disciplina 512/.55
Collana History of Mathematics
Soggetto topico Lie groups - History
Linear algebraic groups - History
Soggetto genere / forma Electronic books.
ISBN 1-4704-3889-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910480532003321
Borel Armand  
Providence, Rhode Island : , : American Mathematical Society : , : London Mathematical Society, , 2001
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Essays in the history of Lie groups and algebraic groups / / Armand Borel
Essays in the history of Lie groups and algebraic groups / / Armand Borel
Autore Borel Armand
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society : , : London Mathematical Society, , 2001
Descrizione fisica 1 online resource (185 pages) : illustrations, photographs
Disciplina 512/.55
Collana History of Mathematics
Soggetto topico Lie groups - History
Linear algebraic groups - History
ISBN 1-4704-3889-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910794725503321
Borel Armand  
Providence, Rhode Island : , : American Mathematical Society : , : London Mathematical Society, , 2001
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Essays in the history of Lie groups and algebraic groups / / Armand Borel
Essays in the history of Lie groups and algebraic groups / / Armand Borel
Autore Borel Armand
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society : , : London Mathematical Society, , 2001
Descrizione fisica 1 online resource (185 pages) : illustrations, photographs
Disciplina 512/.55
Collana History of Mathematics
Soggetto topico Lie groups - History
Linear algebraic groups - History
ISBN 1-4704-3889-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910808471403321
Borel Armand  
Providence, Rhode Island : , : American Mathematical Society : , : London Mathematical Society, , 2001
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear Algebraic Groups [[electronic resource] /] / by Armand Borel
Linear Algebraic Groups [[electronic resource] /] / by Armand Borel
Autore Borel Armand
Edizione [2nd ed. 1991.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1991
Descrizione fisica 1 online resource (XI, 290 p.)
Disciplina 512.55
512.482
Collana Graduate Texts in Mathematics
Soggetto topico Topological groups
Lie groups
Topological Groups, Lie Groups
ISBN 1-4612-0941-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto AG—Background Material From Algebraic Geometry -- §1. Some Topological Notions -- §2. Some Facts from Field Theory -- §3. Some Commutative Algebra -- §4. Sheaves -- §5. Affine K-Schemes, Prevarieties -- §6. Products; Varieties -- §7. Projective and Complete Varieties -- §8. Rational Functions; Dominant Morphisms -- §9. Dimension -- §10. Images and Fibres of a Morphism -- §11. k-structures on K-Schemes -- §12. k-Structures on Varieties -- §13. Separable points -- §14. Galois Criteria for Rationality -- §15. Derivations and Differentials -- §16. Tangent Spaces -- §17. Simple Points -- §18. Normal Varieties -- References -- I—General Notions Associated With Algebraic Groups -- §1. The Notion of an Algebraic Groups -- §2. Group Closure; Solvable and Nilpotent Groups -- §3. The Lie Algebra of an Algebraic Group -- §4. Jordan Decomposition -- II — Homogeneous Spaces -- §5. Semi-Invariants -- §6. Homogeneous Spaces -- §7. Algebraic Groups in Characteristic Zero -- III Solvable Groups -- §8. Diagonalizable Groups and Tori -- §9. Conjugacy Classes and Centralizers of Semi-Simple Elements -- §10. Connected Solvable Groups -- IV—Borel Subgroups; Reductive Groups -- §11. Borel Subgroups -- §12. Cartan Subgroups; Regular Elements -- §13. The Borel Subgroups Containing a Given Torus -- §14. Root Systems and Bruhat Decomposition in Reductive Groups -- V—Rationality Questions -- §15. Split Solvable Groups and Subgroups -- §16. Groups over Finite Fields -- §17. Quotient of a Group by a Lie Subalgebra -- §18. Cartan Subgroups over the Groundfield. Unirationality. Splitting of Reductive Groups -- §19. Cartan Subgroups of Solvable Groups -- §20. Isotropic Reductive Groups -- §21. Relative Root System and Bruhat Decomposition for Isotropic Reductive Groups -- §22. Central Isogenies -- §23. Examples -- §24. Survey of Some Other Topics -- A. Classification -- B. Linear Representations -- C. Real Reductive Groups -- References for Chapters I to V -- Index of Definition -- Index of Notation.
Record Nr. UNINA-9910480073703321
Borel Armand  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1991
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear Algebraic Groups [[electronic resource] /] / by Armand Borel
Linear Algebraic Groups [[electronic resource] /] / by Armand Borel
Autore Borel Armand
Edizione [2nd ed. 1991.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1991
Descrizione fisica 1 online resource (XI, 290 p.)
Disciplina 512.55
512.482
Collana Graduate Texts in Mathematics
Soggetto topico Topological groups
Lie groups
Topological Groups, Lie Groups
ISBN 1-4612-0941-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto AG—Background Material From Algebraic Geometry -- §1. Some Topological Notions -- §2. Some Facts from Field Theory -- §3. Some Commutative Algebra -- §4. Sheaves -- §5. Affine K-Schemes, Prevarieties -- §6. Products; Varieties -- §7. Projective and Complete Varieties -- §8. Rational Functions; Dominant Morphisms -- §9. Dimension -- §10. Images and Fibres of a Morphism -- §11. k-structures on K-Schemes -- §12. k-Structures on Varieties -- §13. Separable points -- §14. Galois Criteria for Rationality -- §15. Derivations and Differentials -- §16. Tangent Spaces -- §17. Simple Points -- §18. Normal Varieties -- References -- I—General Notions Associated With Algebraic Groups -- §1. The Notion of an Algebraic Groups -- §2. Group Closure; Solvable and Nilpotent Groups -- §3. The Lie Algebra of an Algebraic Group -- §4. Jordan Decomposition -- II — Homogeneous Spaces -- §5. Semi-Invariants -- §6. Homogeneous Spaces -- §7. Algebraic Groups in Characteristic Zero -- III Solvable Groups -- §8. Diagonalizable Groups and Tori -- §9. Conjugacy Classes and Centralizers of Semi-Simple Elements -- §10. Connected Solvable Groups -- IV—Borel Subgroups; Reductive Groups -- §11. Borel Subgroups -- §12. Cartan Subgroups; Regular Elements -- §13. The Borel Subgroups Containing a Given Torus -- §14. Root Systems and Bruhat Decomposition in Reductive Groups -- V—Rationality Questions -- §15. Split Solvable Groups and Subgroups -- §16. Groups over Finite Fields -- §17. Quotient of a Group by a Lie Subalgebra -- §18. Cartan Subgroups over the Groundfield. Unirationality. Splitting of Reductive Groups -- §19. Cartan Subgroups of Solvable Groups -- §20. Isotropic Reductive Groups -- §21. Relative Root System and Bruhat Decomposition for Isotropic Reductive Groups -- §22. Central Isogenies -- §23. Examples -- §24. Survey of Some Other Topics -- A. Classification -- B. Linear Representations -- C. Real Reductive Groups -- References for Chapters I to V -- Index of Definition -- Index of Notation.
Record Nr. UNINA-9910789343503321
Borel Armand  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1991
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear Algebraic Groups / / by Armand Borel
Linear Algebraic Groups / / by Armand Borel
Autore Borel Armand
Edizione [2nd ed. 1991.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1991
Descrizione fisica 1 online resource (XI, 290 p.)
Disciplina 512.55
512.482
Collana Graduate Texts in Mathematics
Soggetto topico Topological groups
Lie groups
Topological Groups, Lie Groups
ISBN 1-4612-0941-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto AG—Background Material From Algebraic Geometry -- §1. Some Topological Notions -- §2. Some Facts from Field Theory -- §3. Some Commutative Algebra -- §4. Sheaves -- §5. Affine K-Schemes, Prevarieties -- §6. Products; Varieties -- §7. Projective and Complete Varieties -- §8. Rational Functions; Dominant Morphisms -- §9. Dimension -- §10. Images and Fibres of a Morphism -- §11. k-structures on K-Schemes -- §12. k-Structures on Varieties -- §13. Separable points -- §14. Galois Criteria for Rationality -- §15. Derivations and Differentials -- §16. Tangent Spaces -- §17. Simple Points -- §18. Normal Varieties -- References -- I—General Notions Associated With Algebraic Groups -- §1. The Notion of an Algebraic Groups -- §2. Group Closure; Solvable and Nilpotent Groups -- §3. The Lie Algebra of an Algebraic Group -- §4. Jordan Decomposition -- II — Homogeneous Spaces -- §5. Semi-Invariants -- §6. Homogeneous Spaces -- §7. Algebraic Groups in Characteristic Zero -- III Solvable Groups -- §8. Diagonalizable Groups and Tori -- §9. Conjugacy Classes and Centralizers of Semi-Simple Elements -- §10. Connected Solvable Groups -- IV—Borel Subgroups; Reductive Groups -- §11. Borel Subgroups -- §12. Cartan Subgroups; Regular Elements -- §13. The Borel Subgroups Containing a Given Torus -- §14. Root Systems and Bruhat Decomposition in Reductive Groups -- V—Rationality Questions -- §15. Split Solvable Groups and Subgroups -- §16. Groups over Finite Fields -- §17. Quotient of a Group by a Lie Subalgebra -- §18. Cartan Subgroups over the Groundfield. Unirationality. Splitting of Reductive Groups -- §19. Cartan Subgroups of Solvable Groups -- §20. Isotropic Reductive Groups -- §21. Relative Root System and Bruhat Decomposition for Isotropic Reductive Groups -- §22. Central Isogenies -- §23. Examples -- §24. Survey of Some Other Topics -- A. Classification -- B. Linear Representations -- C. Real Reductive Groups -- References for Chapters I to V -- Index of Definition -- Index of Notation.
Record Nr. UNINA-9910828775803321
Borel Armand  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1991
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui