### Abstract

Kashina, Montgomery and Ng introduced the n-th indicator ν_{n}(H) of a finite-dimensional Hopf algebra H and showed that the indicators have some interesting properties such as the gauge invariance. The aim of this paper is to investigate the properties of ν_{n}’s. In particular, we obtain the cyclotomic integrality of ν_{n} and a formula for ν_{n} of the Drinfeld double. Our results are applied to the finite-dimensional pointed Hopf algebra u(D, λ, µ) introduced by Andruskiewitsch and Schneider. As an application, we obtain the second indicator of u_{q}(sl_{2}) and show that if p and q are roots of unity of the same order, then u_{p}(sl_{2}) and u_{q}(sl_{2}) are gauge equivalent if and only if q = p, where p and q are roots of unity of the same odd order.

Original language | English |
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Pages (from-to) | 155-201 |

Number of pages | 47 |

Journal | Israel Journal of Mathematics |

Volume | 207 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 Feb 17 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Israel Journal of Mathematics*,

*207*(1), 155-201. https://doi.org/10.1007/s11856-015-1156-x