An analogue of a reductive algebraic monoid whose unit group is a Kac-Moody group
著者
書誌事項
An analogue of a reductive algebraic monoid whose unit group is a Kac-Moody group
（Memoirs of the American Mathematical Society, no. 823）
American Mathematical Society, 2005
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注記
"Volume 174, number 823 (third of 4 numbers)"
Includes bibliographical references (p. 89-90)
内容説明・目次
内容説明
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.
目次
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.
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