# Hopf Powers and Orders for Some Bismash Products

Research paper by Rachel Landers, Susan Montgomery, Peter Schauenburg

Indexed on: 21 May '04Published on: 21 May '04Published in: Mathematics - Quantum Algebra

#### Abstract

The Hopf order of an element $h$ of a Hopf algebra $H$ is the least $n$ such that the $n$-th Hopf power of $h$ is trivial. For some bismash product Hopf algebras obtained from factorizable groups (including Drinfeld doubles of some groups) we compute the dimensions of the spaces of elements with trivial $n$-th Hopf powers, and determine which Hopf orders of elements are possible. We discuss the behavior under twists and duality.