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Univ. Federico II (18)

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Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan

Borel Armand

Providence, Rhode Island : , : American Mathematical Society, , [2002]

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Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan

Borel Armand

Providence, Rhode Island : , : American Mathematical Society, , [2002]

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Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan

Borel Armand

Providence, Rhode Island : , : American Mathematical Society, , [2002]

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Extended affine Lie algebras and their root systems / / Bruce N. Allison [and four others]

Allison Bruce N (Bruce Normansell), <1945->

Providence, Rhode Island : , : American Mathematical Society, , [1997]

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Extended affine Lie algebras and their root systems / / Bruce N. Allison [and four others]

Allison Bruce N (Bruce Normansell), <1945->

Providence, Rhode Island : , : American Mathematical Society, , [1997]

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Extended affine Lie algebras and their root systems / / Bruce N. Allison [and four others]

Allison Bruce N (Bruce Normansell), <1945->

Providence, Rhode Island : , : American Mathematical Society, , [1997]

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Locally finite root systems / / Ottmar Loos, Erhard Neher

Loos Ottmar

Providence, Rhode Island : , : American Mathematical Society, , 2004

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Locally finite root systems / / Ottmar Loos, Erhard Neher

Loos Ottmar

Providence, Rhode Island : , : American Mathematical Society, , 2004

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Locally finite root systems / / Ottmar Loos, Erhard Neher

Loos Ottmar

Providence, Rhode Island : , : American Mathematical Society, , 2004

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Maximal abelian sets of roots / / R. Lawther

Lawther R (Ross), <1960->

Providence, Rhode Island : , : American Mathematical Society, , 2017

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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

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

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

Autore	Allison Bruce N (Bruce Normansell), <1945->
Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , [1997]
Descrizione fisica	1 online resource (138 p.)
Disciplina	510 s 512/.55
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Infinite dimensional Lie algebras Kac-Moody algebras Root systems (Algebra)
Soggetto genere / forma	Electronic books.
ISBN	1-4704-0188-6
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Record Nr.	UNINA-9910480216803321

Autore	Allison Bruce N (Bruce Normansell), <1945->
Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , [1997]
Descrizione fisica	1 online resource (138 p.)
Disciplina	510 s 512/.55
Altri autori (Persone)	AllisonBruce N <1945-> (Bruce Normansell)
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Infinite dimensional Lie algebras Kac-Moody algebras Root systems (Algebra)
ISBN	1-4704-0188-6
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Record Nr.	UNINA-9910788731603321

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Autore	Loos Ottmar
Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , 2004
Descrizione fisica	1 online resource (232 p.)
Disciplina	512/.482
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Lie superalgebras Root systems (Algebra)
Soggetto genere / forma	Electronic books.
ISBN	1-4704-0412-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Contents""; ""Introduction""; ""1. The category of sets in vector spaces""; ""2. Finiteness conditions and bases""; ""3. Locally finite root systems""; ""4. Invariant inner products and the coroot system""; ""5. Weyl groups""; ""6. Integral bases, root bases and Dynkin diagrams""; ""7. Weights and coweights""; ""8. Classification""; ""9. More on Weyl groups and automorphism groups""; ""10. Parabolic subsets and positive systems for symmetric sets in vector spaces""; ""11. Parabolic subsets of root systems and presentations of the root lattice and the Weyl group"" ""12. Closed and full subsystems of finite and infinite classical root systems""""13. Parabolic subsets of root systems: classification""; ""14. Positive systems in root systems""; ""15. Positive linear forms and facets""; ""16. Dominant and fundamental weights""; ""17. Gradings of root systems""; ""18. Elementary relations and graphs in 3-graded root systems""; ""Appendix A. Some standard results on finite root systems""; ""Appendix B. Cones defined by totally preordered sets""; ""Bibliography""; ""Index of notations""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I"" ""J""""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""W""; ""Z""
Record Nr.	UNINA-9910480515603321

Autore	Loos Ottmar
Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , 2004
Descrizione fisica	1 online resource (232 p.)
Disciplina	512/.482
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Lie superalgebras Root systems (Algebra)
ISBN	1-4704-0412-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Contents""; ""Introduction""; ""1. The category of sets in vector spaces""; ""2. Finiteness conditions and bases""; ""3. Locally finite root systems""; ""4. Invariant inner products and the coroot system""; ""5. Weyl groups""; ""6. Integral bases, root bases and Dynkin diagrams""; ""7. Weights and coweights""; ""8. Classification""; ""9. More on Weyl groups and automorphism groups""; ""10. Parabolic subsets and positive systems for symmetric sets in vector spaces""; ""11. Parabolic subsets of root systems and presentations of the root lattice and the Weyl group"" ""12. Closed and full subsystems of finite and infinite classical root systems""""13. Parabolic subsets of root systems: classification""; ""14. Positive systems in root systems""; ""15. Positive linear forms and facets""; ""16. Dominant and fundamental weights""; ""17. Gradings of root systems""; ""18. Elementary relations and graphs in 3-graded root systems""; ""Appendix A. Some standard results on finite root systems""; ""Appendix B. Cones defined by totally preordered sets""; ""Bibliography""; ""Index of notations""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I"" ""J""""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""W""; ""Z""
Record Nr.	UNINA-9910788747403321

Autore	Loos Ottmar
Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , 2004
Descrizione fisica	1 online resource (232 p.)
Disciplina	512/.482
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Lie superalgebras Root systems (Algebra)
ISBN	1-4704-0412-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Contents""; ""Introduction""; ""1. The category of sets in vector spaces""; ""2. Finiteness conditions and bases""; ""3. Locally finite root systems""; ""4. Invariant inner products and the coroot system""; ""5. Weyl groups""; ""6. Integral bases, root bases and Dynkin diagrams""; ""7. Weights and coweights""; ""8. Classification""; ""9. More on Weyl groups and automorphism groups""; ""10. Parabolic subsets and positive systems for symmetric sets in vector spaces""; ""11. Parabolic subsets of root systems and presentations of the root lattice and the Weyl group"" ""12. Closed and full subsystems of finite and infinite classical root systems""""13. Parabolic subsets of root systems: classification""; ""14. Positive systems in root systems""; ""15. Positive linear forms and facets""; ""16. Dominant and fundamental weights""; ""17. Gradings of root systems""; ""18. Elementary relations and graphs in 3-graded root systems""; ""Appendix A. Some standard results on finite root systems""; ""Appendix B. Cones defined by totally preordered sets""; ""Bibliography""; ""Index of notations""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I"" ""J""""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""W""; ""Z""
Record Nr.	UNINA-9910818015503321