On indicators of Hopf algebras

研究成果: Article

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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.

元の言語English
ページ(範囲)155-201
ページ数47
ジャーナルIsrael Journal of Mathematics
207
発行部数1
DOI
出版物ステータスPublished - 2015 2 17
外部発表Yes

ASJC Scopus subject areas

  • Mathematics(all)

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