Affine Kac-Moody groups and Lie algebras in the language of SGA3

In infinite-dimensional Lie theory, the affine Kac-Moody Lie algebras and groups play a distinguished role due to their many applications to various areas of mathematics and physics. Underlying these infinite-dimensional objects there are closely related group schemes and Lie algebras of finite type...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 227; no. 7; p. 107331
Main Authors Morita, Jun, Pianzola, Arturo, Shibata, Taiki
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2023
Subjects
Affine Kac-Moody groups
Loop groups
Semisimple group schemes
Twisted Chevalley groups
secondary
Twisted Chevalley groups
Loop groups
Semisimple group schemes
Affine Kac-Moody groups
Primary
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Summary:In infinite-dimensional Lie theory, the affine Kac-Moody Lie algebras and groups play a distinguished role due to their many applications to various areas of mathematics and physics. Underlying these infinite-dimensional objects there are closely related group schemes and Lie algebras of finite type over Laurent polynomial rings. The language of SGA3 is perfectly suited to describe such objects. The purpose of this short article is to provide a natural description of the affine Kac-Moody groups and Lie algebras using this language.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2023.107331