---
_id: '7940'
abstract:
- lang: eng
  text: We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody
    Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter
    is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras.
    As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this
    class of affine Yangians. Another independent proof of the PBW theorem is given
    recently by Guay, Regelskis, and Wendlandt [GRW18].
acknowledgement: Gufang Zhao is affiliated to IST Austria, Hausel group until July
  of 2018. Supported by the Advanced Grant Arithmetic and Physics of Higgs moduli
  spaces No. 320593 of the European Research Council.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yaping
  full_name: Yang, Yaping
  id: 360D8648-F248-11E8-B48F-1D18A9856A87
  last_name: Yang
- first_name: Gufang
  full_name: Zhao, Gufang
  id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
  last_name: Zhao
citation:
  ama: Yang Y, Zhao G. The PBW theorem for affine Yangians. <i>Transformation Groups</i>.
    2020;25:1371-1385. doi:<a href="https://doi.org/10.1007/s00031-020-09572-6">10.1007/s00031-020-09572-6</a>
  apa: Yang, Y., &#38; Zhao, G. (2020). The PBW theorem for affine Yangians. <i>Transformation
    Groups</i>. Springer Nature. <a href="https://doi.org/10.1007/s00031-020-09572-6">https://doi.org/10.1007/s00031-020-09572-6</a>
  chicago: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” <i>Transformation
    Groups</i>. Springer Nature, 2020. <a href="https://doi.org/10.1007/s00031-020-09572-6">https://doi.org/10.1007/s00031-020-09572-6</a>.
  ieee: Y. Yang and G. Zhao, “The PBW theorem for affine Yangians,” <i>Transformation
    Groups</i>, vol. 25. Springer Nature, pp. 1371–1385, 2020.
  ista: Yang Y, Zhao G. 2020. The PBW theorem for affine Yangians. Transformation
    Groups. 25, 1371–1385.
  mla: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” <i>Transformation
    Groups</i>, vol. 25, Springer Nature, 2020, pp. 1371–85, doi:<a href="https://doi.org/10.1007/s00031-020-09572-6">10.1007/s00031-020-09572-6</a>.
  short: Y. Yang, G. Zhao, Transformation Groups 25 (2020) 1371–1385.
date_created: 2020-06-07T22:00:55Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2023-08-21T07:06:21Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00031-020-09572-6
ec_funded: 1
external_id:
  arxiv:
  - '1804.04375'
  isi:
  - '000534874300003'
intvolume: '        25'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1804.04375
month: '12'
oa: 1
oa_version: Preprint
page: 1371-1385
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '320593'
  name: Arithmetic and physics of Higgs moduli spaces
publication: Transformation Groups
publication_identifier:
  eissn:
  - 1531586X
  issn:
  - '10834362'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The PBW theorem for affine Yangians
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
year: '2020'
...