Birational Equivalences and Generalized Weyl Algebras

Atabey Kaygun

doi:10.3842/SIGMA.2025.063

Birational Equivalences and Generalized Weyl Algebras

Atabey Kaygun^*

^*Corresponding author for this work

Department of Mathematics Engineering

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

Abstract

We calculate suitably localized Hochschild homologies of various quantum groups and Podleś spheres after realizing them as generalized Weyl algebras (GWAs). We use the fact that every GWA is birationally equivalent to a smash product with a 1-torus. We also address and solve the birational equivalence problem, and the birational smoothness problem for GWAs.

Original language	English
Article number	063
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	21
DOIs	https://doi.org/10.3842/SIGMA.2025.063
Publication status	Published - 2025

Bibliographical note

Publisher Copyright:
© 2025, Institute of Mathematics. All rights reserved.

Keywords

Hochschild homology
Podleś spheres
generalized Weyl algebras
noncommutative birational equivalences
quantum enveloping algebras
quantum groups

Access to Document

10.3842/SIGMA.2025.063

Cite this

@article{b80c18f6918640c9a1da417a8950e257,

title = "Birational Equivalences and Generalized Weyl Algebras",

abstract = "We calculate suitably localized Hochschild homologies of various quantum groups and Podle{\'s} spheres after realizing them as generalized Weyl algebras (GWAs). We use the fact that every GWA is birationally equivalent to a smash product with a 1-torus. We also address and solve the birational equivalence problem, and the birational smoothness problem for GWAs.",

keywords = "Hochschild homology, Podle{\'s} spheres, generalized Weyl algebras, noncommutative birational equivalences, quantum enveloping algebras, quantum groups",

author = "Atabey Kaygun",

year = "2025",

doi = "10.3842/SIGMA.2025.063",

language = "English",

volume = "21",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

issn = "1815-0659",

publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

TY - JOUR

T1 - Birational Equivalences and Generalized Weyl Algebras

AU - Kaygun, Atabey

PY - 2025

Y1 - 2025

N2 - We calculate suitably localized Hochschild homologies of various quantum groups and Podleś spheres after realizing them as generalized Weyl algebras (GWAs). We use the fact that every GWA is birationally equivalent to a smash product with a 1-torus. We also address and solve the birational equivalence problem, and the birational smoothness problem for GWAs.

AB - We calculate suitably localized Hochschild homologies of various quantum groups and Podleś spheres after realizing them as generalized Weyl algebras (GWAs). We use the fact that every GWA is birationally equivalent to a smash product with a 1-torus. We also address and solve the birational equivalence problem, and the birational smoothness problem for GWAs.

KW - Hochschild homology

KW - Podleś spheres

KW - generalized Weyl algebras

KW - noncommutative birational equivalences

KW - quantum enveloping algebras

KW - quantum groups

UR - https://www.scopus.com/pages/publications/105012768117

U2 - 10.3842/SIGMA.2025.063

DO - 10.3842/SIGMA.2025.063

M3 - Article

AN - SCOPUS:105012768117

SN - 1815-0659

VL - 21

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 063

ER -

Birational Equivalences and Generalized Weyl Algebras

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this