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An analogue of a reductive algebraic monoid whose unit group is a Kac-Moody group / Claus Mokler.
- Format:
- Book
- Author/Creator:
- Mokler, Claus, 1962- author.
- Series:
- Memoirs of the American Mathematical Society ; no. 823.
- Memoirs of the American Mathematical Society, 0065-9266 ; number 823
- Language:
- English
- Subjects (All):
- Kac-Moody algebras.
- Lie groups.
- Algebroids.
- Physical Description:
- 1 online resource (104 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, 2005.
- Language Note:
- English
- Summary:
- 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.
- Contents:
- ""Contents""; ""Introduction""; ""Contents""; ""Chapter 1. Preliminaries""; ""1.1. Kac-Moody algebras, Kac-Moody groups and the algebra of strongly regular functions""; ""1.2. A generalization of affine toric varieties""; ""Chapter 2. The monoid G and its structure""; ""2.1. The face lattice of the Tits cone""; ""2.2. The definition of the monoid G""; ""2.3. Formulas for computations in G""; ""2.4. The unit regularity of G""; ""2.5. The Weyl monoid W and the monoids T, N""; ""2.6. Some double coset partitions of G""; ""2.7. Constructing G from the twin root datum""
- Notes:
- "Volume 174, number 823 (third of 4 numbers)."
- Includes bibliographical references (pages 89-90).
- Description based on print version record.
- ISBN:
- 1-4704-0424-9
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