Hopf algebras of dimension 16

TL;DR

This paper completes the classification of 16-dimensional Hopf algebras over an algebraically closed field of characteristic zero, identifying their structural properties and duality characteristics.

Contribution

It provides a complete classification of Hopf algebras of dimension 16, highlighting the conditions under which they are semisimple, pointed, or have the Chevalley property.

Findings

Non-semisimple Hopf algebras of dimension 16 have the Chevalley property or their duals are pointed.

The classification confirms all such algebras over algebraically closed fields of characteristic zero.

The results extend the understanding of low-dimensional Hopf algebra structures.

Abstract

We complete the classification of Hopf algebras of dimension 16 over an algebraically closed field of characteristic zero. We show that a non-semisimple Hopf algebra of dimension 16, has either the Chevalley property or its dual is pointed.