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

DOI10.1016/j.jpaa.2023.107331OpenAlexW4313897538MaRDI QIDQ2690461

Taiki Shibata, Jun Morita, Arturo Pianzola

Publication date: 17 March 2023

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.12727

zbMATH Keywords

loop groupsaffine Kac-Moody groupstwisted Chevalley groupssemisimple group schemes

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Loop groups and related constructions, group-theoretic treatment (22E67) Group schemes (14L15) Kac-Moody groups (20G44)

Cites Work

• Vanishing of \(H^1\) for Dedekind rings and applications to loop algebras
• Uniqueness and presentation of Kac-Moody groups over fields
• Twisted loop groups and their affine flag varieties. With an appendix by T. Haines and M. Rapoport.
• Théorie de la descente et algèbres d'Azumaya
• Kac-Moody groups, their flag varieties and representation theory
• A new class of Lie algebras
• Schémas en groupes. III: Structure des schémas en groupes réductifs. Exposés XIX à XXVI. Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3), dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• Tits' systems with crystallographic Weyl groups
• Infinite flag varieties and conjugacy theorems
• [https://portal.mardi4nfdi.de/wiki/Publication:5057107 Affine Kac-Moody Groups as Twisted Loop Groups obtained by Galois Descent Considerations]
• Euclidean Lie Algebras
• SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH
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