# An Analogue of a Reductive Algebraic Monoid Whose Unit Group is a Kac-Moody Group (Memoirs of the American Mathematical Society No. 174)

By: Claus Mokler (editor)Paperback

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### Description

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

Introduction Preliminaries The monoid $\widehat{G}$ and its structure An algebraic geometric setting A generalized Tannaka-Krein reconstruction The proof of $\overline{G}=\widehat{G}$ and some other theorems The proof of Lie$(\overline{G})\cong \mathbf g$ Bibliography.

### Product Details

• publication date: 15/01/2005
• ISBN13: 9780821836484
• Format: Paperback
• Number Of Pages: 90
• ID: 9780821836484
• weight: 227
• ISBN10: 082183648X

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