On twisting of finite-dimensional Hopf algebras

Details On twisting of finite-dimensional Hopf algebras On twisting of finite-dimensional Hopf algebras

2001-07-23

arxiv.org/abs/math/0107167v2

J. Algebra 256 (2002), no. 2, 484--501

Mathematics

Quantum Algebra

14 pages, AMS-Latex. In Section 5 several results were improved and simplified. Minor errors corrected and several references

Scientific paper

In this paper we study the properties of Drinfeld's twisting for finite-dimensional Hopf algebras. We determine how the integral of the dual to a unimodular Hopf algebra $H$ changes under twisting of $H$. We show that the classes of cosemisimple unimodular, cosemisimple involutive, cosemisimple quasitriangular finite-dimensional Hopf algebras are stable under twisting. We also prove the cosemisimplicity of a coalgebra obtained by twisting of a cosemisimple unimodular Hopf algebra by two different twists on two sides (such twists are closely related to biGalois extensions), and describe the representation theory of its dual. Next, we define the notion of a non-degenerate twist for a Hopf algebra $H$, and set up a bijection between such twists for $H$ and $H^*$. This bijection is based on Miyashita-Ulbrich actions of Hopf algebras on simple algebras. It generalizes to the non-commutative case the procedure of inverting a non-degenerate skew-symmetric bilinear form on a vector space. Finally, we apply these results to classification of twists in group algebras and of cosemisimple triangular finite-dimensional Hopf algebras in positive characteristic, generalizing the previously known classification in characteristic zero.

Affiliated with

Also associated with

No associations

Rating

On twisting of finite-dimensional Hopf algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On twisting of finite-dimensional Hopf algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On twisting of finite-dimensional Hopf algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-322715