English

Quasi-Hopf Algebras of Dimension 6

Quantum Algebra 2024-10-07 v1

Abstract

We complete the classification of the 6-dimensional quasi-Hopf algebras, by proving that any such algebra is semisimple. As byproducts, we provide examples of 6-dimensional quasi-bialgebras that are not semisimple as algebras, as well as the concrete quasi-Hopf structures of the 6-dimensional semisimple quasi-Hopf algebras previously classified by Etingof and Gelaki in terms of their category of representations. In total there are 15 quasi-Hopf algebras in dimension 6 which are not pairwise twist equivalent.

Keywords

Cite

@article{arxiv.2410.03476,
  title  = {Quasi-Hopf Algebras of Dimension 6},
  author = {Daniel Bulacu and Matteo Misurati},
  journal= {arXiv preprint arXiv:2410.03476},
  year   = {2024}
}