| eBook ISBN: | 978-1-4704-0424-6 |
| Product Code: | MEMO/174/823.E |
| List Price: | $66.00 |
| MAA Member Price: | $59.40 |
| AMS Member Price: | $39.60 |
| eBook ISBN: | 978-1-4704-0424-6 |
| Product Code: | MEMO/174/823.E |
| List Price: | $66.00 |
| MAA Member Price: | $59.40 |
| AMS Member Price: | $39.60 |
-
Book DetailsMemoirs of the American Mathematical SocietyVolume: 174; 2005; 90 ppMSC: Primary 17; 22
By an easy generalization of the Tannaka-Krein reconstruction we associate to the category of admissible representations of the category \({\mathcal O}\) of a Kac-Moody algebra, and its category of admissible duals, a monoid with a coordinate ring.
The Kac-Moody group is the Zariski open dense unit group of this monoid. The restriction of the coordinate ring to the Kac-Moody group is the algebra of strongly regular functions introduced by V. Kac and D. Peterson.
This monoid has similar structural properties as a reductive algebraic monoid. In particular it is unit regular, its idempotents related to the faces of the Tits cone. It has Bruhat and Birkhoff decompositions.
The Kac-Moody algebra is isomorphic to the Lie algebra of this monoid.
-
Table of Contents
-
Chapters
-
Introduction
-
1. Preliminaries
-
2. The monoid $\hat {G}$ and its structure
-
3. An algebraic geometric setting
-
4. A generalized Tannaka-Krein reconstruction
-
5. The proof of $\bar {G} = \hat {G}$ and some other theorems
-
6. The proof of $\operatorname {Lie}(\bar {G}) \cong \mathbf {g}$
-
-
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
By an easy generalization of the Tannaka-Krein reconstruction we associate to the category of admissible representations of the category \({\mathcal O}\) of a Kac-Moody algebra, and its category of admissible duals, a monoid with a coordinate ring.
The Kac-Moody group is the Zariski open dense unit group of this monoid. The restriction of the coordinate ring to the Kac-Moody group is the algebra of strongly regular functions introduced by V. Kac and D. Peterson.
This monoid has similar structural properties as a reductive algebraic monoid. In particular it is unit regular, its idempotents related to the faces of the Tits cone. It has Bruhat and Birkhoff decompositions.
The Kac-Moody algebra is isomorphic to the Lie algebra of this monoid.
-
Chapters
-
Introduction
-
1. Preliminaries
-
2. The monoid $\hat {G}$ and its structure
-
3. An algebraic geometric setting
-
4. A generalized Tannaka-Krein reconstruction
-
5. The proof of $\bar {G} = \hat {G}$ and some other theorems
-
6. The proof of $\operatorname {Lie}(\bar {G}) \cong \mathbf {g}$
