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An Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group
 
Claus Mokler University of Wuppertal, Wuppertal, Germany
An Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group
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
An Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group
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An Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group
Claus Mokler University of Wuppertal, Wuppertal, Germany
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 Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1742005; 90 pp
    MSC: 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 $\operatorname {Lie}(\bar {G}) \cong \mathbf {g}$
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1742005; 90 pp
MSC: 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.

  • 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 $\operatorname {Lie}(\bar {G}) \cong \mathbf {g}$
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.