# Weak integral forms and the sixth Kaplansky conjecture

## TL;DR

This paper proves that finite dimensional semisimple Hopf algebras with a weak integral form are of Frobenius type, connecting integral forms to algebraic structure in the context of the sixth Kaplansky conjecture.

## Contribution

It explicitly states and proves a folklore result linking weak integral forms to Frobenius type in semisimple Hopf algebras, using a historical argument.

## Key findings

- Finite dimensional semisimple Hopf algebras with weak integral forms are of Frobenius type.
- The proof uses an argument similar to Fossum's, predating the Kaplansky conjectures.
- The note clarifies a previously unpublished result referenced by Cuadra and Meir.

## Abstract

It is a short unpublished note from 1998. I make it public because Cuadra and Meir refer to it in their paper. We precisely state and prove a folklore result that if a finite dimensional semisimple Hopf algebra admits a weak integral form then it is of Frobenius type. We use an argument similar to that of Fossum \cite{fos}, which predates the Kaplansky conjectures.