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PreprintarXiv licencearXiv

Coset representatives corresponding to Yetter-Drinfeld modules of modular group and continued fraction

  • Yiwei Zheng
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Abstract

We give complete conjugacy classes of modular group SL(2,Z). Particularly, the conjugacy classes of hyperbolic elements are decided by the proper equivalence classes of indefinite forms, and we give an example. Finally, we describe the coset representatives of centralizer of S, ST, T and hyperbolic elements of SL(2,Z) by regular continued fraction. In conclusion, most Nichols algebras over modular group are infinite-dimensional except Proposition 4.10.

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Cite

BibTeXRIS
BibTeX
@misc{zheng2026coset,
  title = {{Coset representatives corresponding to Yetter-Drinfeld modules of modular group and continued fraction}},
  author = {Yiwei Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.19706},
  eprint = {2607.19706},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.19706},
}
RIS
TY  - UNPB
TI  - Coset representatives corresponding to Yetter-Drinfeld modules of modular group and continued fraction
AU  - Yiwei Zheng
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2607.19706
UR  - https://arxiv.org/abs/2607.19706
AB  - We give complete conjugacy classes of modular group SL(2,Z). Particularly, the conjugacy classes of hyperbolic elements are decided by the proper equivalence classes of indefinite forms, and we give an example. Finally, we describe the coset representatives of centralizer of S, ST, T and hyperbolic elements of SL(2,Z) by regular continued fraction. In conclusion, most Nichols algebras over modular group are infinite-dimensional except Proposition 4.10.
ER  -