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Reflective algebras over factorizable Hopf algebras

  • Rei Sugitani
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Abstract

The reflective algebra (RH(A),Kref(A)), introduced by Laugwitz, Walton and Yakimov, is a quasitriangular left H-comodule algebra constructed from a quasitriangular Hopf algebra (H,R) and a left H-comodule algebra A. We study the structure and factorizability of finite-dimensional reflective algebras. When (H,R) is factorizable, we show that (RH(A),Kref(A)) is isomorphic, as a quasitriangular left H-comodule algebra, to A⊗ H equipped with the trivial left H-coaction on A and the universal K-matrix induced by R21R. In this case, we also classify all universal K-matrices on RH(A). Finally, we prove that (RH(A),Kref(A)) is factorizable if and only if (H,R) is factorizable and A is simple as an algebra.

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Cite

BibTeXRIS
BibTeX
@misc{sugitani2026reflective,
  title = {{Reflective algebras over factorizable Hopf algebras}},
  author = {Rei Sugitani},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04326},
  eprint = {2611.04326},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04326},
}
RIS
TY  - UNPB
TI  - Reflective algebras over factorizable Hopf algebras
AU  - Rei Sugitani
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04326
UR  - https://arxiv.org/abs/2611.04326
AB  - The reflective algebra (R_H(A),K_ref(A)), introduced by Laugwitz, Walton and Yakimov, is a quasitriangular left H-comodule algebra constructed from a quasitriangular Hopf algebra (H,R) and a left H-comodule algebra A. We study the structure and factorizability of finite-dimensional reflective algebras. When (H,R) is factorizable, we show that (R_H(A),K_ref(A)) is isomorphic, as a quasitriangular left H-comodule algebra, to A⊗ H equipped with the trivial left H-coaction on A and the universal K-matrix induced by R_21R. In this case, we also classify all universal K-matrices on R_H(A). Finally, we prove that (R_H(A),K_ref(A)) is factorizable if and only if (H,R) is factorizable and A is simple as an algebra.
ER  -