Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 33 min ago
PreprintarXiv licencearXiv

Generalized quantum cluster structure of reduced Lê--Roger--Yang skein algebras and their Frobenius maps

  • Min Huang
  • Zhihao Wang
Open at sourcePDFDOICite

Abstract

We establish a generalized quantum cluster algebra structure, defined by Bai--Chen--Ding--Xu, on the reduced Lê--Roger--Yang skein algebra of every quasi-triangulable punctured surface. We define Frobenius maps for generalized quantum cluster algebras at roots of unity and use these maps, together with the cluster algebra structure, to construct Frobenius maps for the (reduced) Lê--Roger--Yang skein algebras of all punctured surfaces. As applications of the Frobenius map, we determine the centers of both the Muller--Roger--Yang skein algebras and the reduced Lê--Roger--Yang skein algebras at roots of unity, and compute their ranks as modules over their centers.

Related

  1. Quantum Generalized Cluster Algebras from Scattering Diagrams: Positivity and Mutation
    Huihui Ye
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  2. Integral Forms of Twisted Quantum Affine Algebras and Quantum Frobenius
    Ziyang Jiang, Naihuan Jing
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Discrete C*-Frobenius Algebras and Infinite-Index Extensions in Algebraic Quantum Field Theories
    Ziyun Xu
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsMathematical physicsarXiv
  4. Representations of shifted quantum affine algebras and cluster algebras II: Non simply-laced types and cluster expansions
    Christof Geiss, David Hernandez, Bernard Leclerc
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Rigid dualizing complex for quantum enveloping algebras and algebras of generalized differential operators
    Sophie Chemla
    Journal of AlgebraPeer-reviewedLicence not stated25 citedGeometry & topologyHAL

Cite

BibTeXRIS
BibTeX
@misc{huang2026generalized,
  title = {{Generalized quantum cluster structure of reduced Lê--Roger--Yang skein algebras and their Frobenius maps}},
  author = {Min Huang and Zhihao Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04823},
  eprint = {2610.04823},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04823},
}
RIS
TY  - UNPB
TI  - Generalized quantum cluster structure of reduced Lê--Roger--Yang skein algebras and their Frobenius maps
AU  - Min Huang
AU  - Zhihao Wang
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.04823
UR  - https://arxiv.org/abs/2610.04823
AB  - We establish a generalized quantum cluster algebra structure, defined by Bai--Chen--Ding--Xu, on the reduced Lê--Roger--Yang skein algebra of every quasi-triangulable punctured surface. We define Frobenius maps for generalized quantum cluster algebras at roots of unity and use these maps, together with the cluster algebra structure, to construct Frobenius maps for the (reduced) Lê--Roger--Yang skein algebras of all punctured surfaces. As applications of the Frobenius map, we determine the centers of both the Muller--Roger--Yang skein algebras and the reduced Lê--Roger--Yang skein algebras at roots of unity, and compute their ranks as modules over their centers.
ER  -