Kashina, Montgomery and Ng introduced the n-th indicator νn(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 νn’s. In particular, we obtain the cyclotomic integrality of νn and a formula for νn 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 uq(sl2) and show that if p and q are roots of unity of the same order, then up(sl2) and uq(sl2) are gauge equivalent if and only if q = p, where p and q are roots of unity of the same odd order.
ASJC Scopus subject areas
- 数学 (全般)