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Hopf Powers and Orders for Some Bismash Products

Rachel Landers·Susan Montgomery·Peter Schauenburg
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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.

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Rachel Landers, Susan Montgomery, Peter Schauenburg. 2004-05-21. Hopf Powers and Orders for Some Bismash Products. https://arxiv.org/abs/math/0405408

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