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An Analogue Of A Reductive Algebraic Monoid Whose Unit Group Is A Kac-moody Group (Memoirs of the American Mathematical Society)

Claus Mokler

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ISBN 10: 082183648X / ISBN 13: 9780821836484
Published by American Mathematical Society, 2005
New Condition: New Soft cover
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Brand new. We distribute directly for the publisher. 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. Bookseller Inventory # 1005250165

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Bibliographic Details

Title: An Analogue Of A Reductive Algebraic Monoid ...

Publisher: American Mathematical Society

Publication Date: 2005

Binding: Paperback

Book Condition:New

About this title

Synopsis:

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.

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