Record Nr.

UNINA9910812749903321

Autore

Borel Armand

Titolo

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

Pubbl/distr/stampa


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

ISBN

1-4704-0340-4

Descrizione fisica

1 online resource (153 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 747

Disciplina

510 s

512/.55

Soggetti

Lie groups

Compact groups

Root systems (Algebra)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"Volume 157, number 747 (third of 5 numbers)."

Nota di bibliografia

Includes bibliographical references.

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""