Birational equivalences and Kac-Moody algebras

Atabey Kaygun

doi:10.1016/j.bulsci.2024.103451

Birational equivalences and Kac-Moody algebras

Atabey Kaygun

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Article number	103451
Journal	Bulletin des Sciences Mathematiques
Volume	193
DOIs	https://doi.org/10.1016/j.bulsci.2024.103451
Publication status	Published - Jul 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Masson SAS

Keywords

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

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10.1016/j.bulsci.2024.103451

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title = "Birational equivalences and Kac-Moody algebras",

abstract = "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.",

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AB - 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.

KW - Birational equivalence

KW - Gelfand-Kirillov conjecture

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KW - Quantized Kac-Moody algebras

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VL - 193

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Birational equivalences and Kac-Moody algebras

Abstract

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Keywords

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