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PreprintCC BY-NC-SA 4.0arXiv

Drinfeld presentation of affine iquantum groups via iHopf algebras

  • Ming Lu
  • Xiaolong Pan
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Abstract

Affine quantum groups Ũ and affine iquantum groups Ũimath admit two complementary descriptions: a Serre-type presentation and a Drinfeld (current) presentation. While iquantum groups Ũimath are typically defined via the Serre presentation, their Drinfeld presentations are substantially more subtle and less well understood. In this paper, we give a conceptual derivation of the Drinfeld presentation of Ũimath starting directly from the Drinfeld presentation of Ũ, working within the framework of iHopf algebras. This approach leads naturally to the definition of iquantum affinization associated with arbitrary Kac-Moody algebras g. We further show that, in this general setting, these iquantum affinizations can be realized as coideal subalgebras of quantum affinizations with respect to the Drinfeld coproduct. Finally, in the affine case, we describe the imaginary root vectors Θi,r of Ũimath explicitly in terms of the root vectors ψ±i,r of Ũ, thereby extending the results of Li and Przeździecki for certain affine types of Ũimath.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026drinfeld,
  title = {{Drinfeld presentation of affine iquantum groups via iHopf algebras}},
  author = {Ming Lu and Xiaolong Pan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30521},
  eprint = {2610.30521},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30521},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Drinfeld presentation of affine iquantum groups via iHopf algebras
AU  - Ming Lu
AU  - Xiaolong Pan
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30521
UR  - https://arxiv.org/abs/2610.30521
AB  - Affine quantum groups Ũ and affine iquantum groups Ũ^imath admit two complementary descriptions: a Serre-type presentation and a Drinfeld (current) presentation. While iquantum groups Ũ^imath are typically defined via the Serre presentation, their Drinfeld presentations are substantially more subtle and less well understood. In this paper, we give a conceptual derivation of the Drinfeld presentation of Ũ^imath starting directly from the Drinfeld presentation of Ũ, working within the framework of iHopf algebras. This approach leads naturally to the definition of iquantum affinization associated with arbitrary Kac-Moody algebras g. We further show that, in this general setting, these iquantum affinizations can be realized as coideal subalgebras of quantum affinizations with respect to the Drinfeld coproduct. Finally, in the affine case, we describe the imaginary root vectors Θ_i,r of Ũ^imath explicitly in terms of the root vectors ψ^±_i,r of Ũ, thereby extending the results of Li and Przeździecki for certain affine types of Ũ^imath.
ER  -