Birational equivalences and Kac-Moody algebras

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We show that every Kac-Moody algebra is birationally equivalent to a smash biproduct of two copies of a Weyl algebra together with a polynomial algebra. We also show that the same is true for quantized Kac-Moody algebras where one replaces Weyl algebras with their quantum analogues.

Original languageEnglish
Article number103451
JournalBulletin des Sciences Mathematiques
Publication statusPublished - Jul 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Masson SAS


  • Birational equivalence
  • Gelfand-Kirillov conjecture
  • Kac-Moody algebras
  • Quantized Kac-Moody algebras


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