eBook ISBN:  9781470404246 
Product Code:  MEMO/174/823.E 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $39.60 
eBook ISBN:  9781470404246 
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 TannakaKrein reconstruction we associate to the category of admissible representations of the category \({\mathcal O}\) of a KacMoody algebra, and its category of admissible duals, a monoid with a coordinate ring.
The KacMoody group is the Zariski open dense unit group of this monoid. The restriction of the coordinate ring to the KacMoody 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 KacMoody 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 TannakaKrein reconstruction

5. The proof of $\bar {G} = \hat {G}$ and some other theorems

6. The proof of $\operatorname {Lie}(\bar {G}) \cong \mathbf {g}$


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By an easy generalization of the TannakaKrein reconstruction we associate to the category of admissible representations of the category \({\mathcal O}\) of a KacMoody algebra, and its category of admissible duals, a monoid with a coordinate ring.
The KacMoody group is the Zariski open dense unit group of this monoid. The restriction of the coordinate ring to the KacMoody 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 KacMoody 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 TannakaKrein reconstruction

5. The proof of $\bar {G} = \hat {G}$ and some other theorems

6. The proof of $\operatorname {Lie}(\bar {G}) \cong \mathbf {g}$