| eBook ISBN: | 978-1-4704-0340-9 |
| Product Code: | MEMO/157/747.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $39.00 |
| eBook ISBN: | 978-1-4704-0340-9 |
| Product Code: | MEMO/157/747.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $39.00 |
-
Book DetailsMemoirs of the American Mathematical SocietyVolume: 157; 2002; 136 ppMSC: Primary 22; 17; Secondary 57
We describe the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in terms of the extended Dynkin diagram of the simply connected cover, together with the coroot integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.
ReadershipGraduate students and research mathematicians interested in topological groups, Lie groups, and nonassociative rings and algebras.
-
Table of Contents
-
Chapters
-
1. Introduction
-
2. Almost commuting $N$-tuples
-
3. Some characterizations of groups of type $A$
-
4. $c$-pairs
-
5. Commuting triples
-
6. Some results on diagram automorphisms and associated root systems
-
7. The fixed subgroup of an automorphism
-
8. $C$-triples
-
9. The tori $\bar {S}(k)$ and $\bar {S}^{w_C}(\bar {\mathbf {g}},k)$ and their Weyl groups
-
10. The Chern-Simons invariant
-
11. The case when $\langle C\rangle $ is not cyclic
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
We describe the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in terms of the extended Dynkin diagram of the simply connected cover, together with the coroot integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.
Graduate students and research mathematicians interested in topological groups, Lie groups, and nonassociative rings and algebras.
-
Chapters
-
1. Introduction
-
2. Almost commuting $N$-tuples
-
3. Some characterizations of groups of type $A$
-
4. $c$-pairs
-
5. Commuting triples
-
6. Some results on diagram automorphisms and associated root systems
-
7. The fixed subgroup of an automorphism
-
8. $C$-triples
-
9. The tori $\bar {S}(k)$ and $\bar {S}^{w_C}(\bar {\mathbf {g}},k)$ and their Weyl groups
-
10. The Chern-Simons invariant
-
11. The case when $\langle C\rangle $ is not cyclic
