Note on infinite iterated crossed products of Hopf algebras and the Drinfeld double

TL;DR

This paper characterizes the Drinfeld double of a finite dimensional Hopf algebra as the natural infinite crossed product, providing a new perspective on the structure of Hopf algebras.

Contribution

It establishes that the infinite crossed product associated with a finite dimensional Hopf algebra is precisely its Drinfeld double, offering a novel characterization.

Findings

Infinite crossed product is the Drinfeld double

Characterization of the Drinfeld double via crossed products

Provides a new structural insight into Hopf algebras

Abstract

For a finite dimensional Hopf algebra we show that an associated natural inclusion of infinite crossed products is the crossed product by the Drinfeld double, and that this is a characterisation of the double.