Examples of inner linear Hopf algebras

TL;DR

This paper explores the concept of inner linear Hopf algebras, providing new criteria and stability results that expand the class of known inner linear Hopf algebras, with implications for related inner unitary structures.

Contribution

It introduces two general results: a characterization via Hopf duals and a stability result under extensions, broadening the understanding of inner linear Hopf algebras.

Findings

Characterization of inner linear Hopf algebras using Hopf duals

Stability of inner linearity under algebra extensions

Discussion of inner unitary Hopf *-algebras

Abstract

The notion of inner linear Hopf algebra is a generalization of the notion of discrete linear group. In this paper, we prove two general results that enable us to enlarge the class of Hopf algebras that are known to be inner linear: the first one is a characterization by using the Hopf dual, while the second one is a stability result under extensions. We also discuss the related notion of inner unitary Hopf *-algebra.