Skip to content
DraconiticResearch
Search Sources API
182,460 studies31 sourcesUpdated 57 min ago
PreprintarXiv licencearXiv

Quantum supersymmetric pairs and the Serre relations via iHopf algebras

  • Jiayi Chen
  • Shiquan Ruan
  • Hongying Zhu
Open at sourcePDFDOICite

Abstract

We study iHopf algebras associated with quantum supergroups of basic type. For a quantum supersymmetric pair (U, Uimath), we realize Uimath and U as the iHopf algebras of the Borel quantum group Ûq≥0 and the tensor product algebra Ûq≥0⊗ Ûq≥0, respectively, while the coideal subalgebra structure is encoded by an embedding between the iHopf algebras. Moreover, we derive an explicit conversion formula between the iHopf multiplication and the original multiplication, which provides a general mechanism transforming the defining relations of quantum (super)groups into relations of iquantum (super)groups. In particular, all the Serre relations that occur in quasi-split iquantum supergroups of basic type are characterized.

Related

  1. Affine supersymmetric pairs
    Andrey Mudrov, Vladimir Stukopin
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Categorical reconstruction of del Pezzo surfaces: Hochschild--Serre algebras and spinor modifications
    Xun Lin, Marco Rampazzo, Shizhuo Zhang
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  3. Free-field realizations of 𝒩 = 1 supersymmetric 𝒲-algebras associated with Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$
    Naozumi Tanabe
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryMathematical physicsarXiv
  4. A Serre-type presentation for imathquantum supergroups of type A
    Weideng Cui, Yaolong Shen
    arXivPreprintCC0Full textAlgebra & number theoryarXiv
  5. Orthogonality graphs of real Cayley-Dickson algebras. Part II: The subgraph on pairs of basis elements
    Svetlana Zhilina
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{chen2026quantum,
  title = {{Quantum supersymmetric pairs and the Serre relations via $\mathrm i$Hopf algebras}},
  author = {Jiayi Chen and Shiquan Ruan and Hongying Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13977},
  eprint = {2609.13977},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13977},
}
RIS
TY  - UNPB
TI  - Quantum supersymmetric pairs and the Serre relations via iHopf algebras
AU  - Jiayi Chen
AU  - Shiquan Ruan
AU  - Hongying Zhu
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.13977
UR  - https://arxiv.org/abs/2609.13977
AB  - We study iHopf algebras associated with quantum supergroups of basic type. For a quantum supersymmetric pair (U, U^imath), we realize U^imath and U as the iHopf algebras of the Borel quantum group Û_q^≥0 and the tensor product algebra Û_q^≥0⊗ Û_q^≥0, respectively, while the coideal subalgebra structure is encoded by an embedding between the iHopf algebras. Moreover, we derive an explicit conversion formula between the iHopf multiplication and the original multiplication, which provides a general mechanism transforming the defining relations of quantum (super)groups into relations of iquantum (super)groups. In particular, all the Serre relations that occur in quasi-split iquantum supergroups of basic type are characterized.
ER  -