Isomorphisms and Automorphisms of Discrete Multiplier Hopf C*-algebras

TL;DR

This paper develops methods to classify and construct isomorphisms of discrete multiplier Hopf C*-algebras using K-theory, revealing new structural insights and automorphism applications.

Contribution

It introduces a K-theoretical approach to construct Hopf algebra isomorphisms and explores automorphisms, including intermediate results on Jordan maps and antipodes.

Findings

Constructed Hopf algebra isomorphisms from K-theoretical data.

Established that Jordan maps of Hopf algebras intertwine antipodes.

Applied results to automorphisms of Hopf algebras.

Abstract

We construct Hopf algebra isomorphisms of discrete multiplier Hopf C*-algebras, and Hopf AF C*-algebras (generalized quantum UHF algebras), from K-theoretical data. Some of the intermediate results are of independent interest, such as a result that Jordan maps of Hopf algebras intertwine antipodes, and the applications to automorphisms of Hopf algebras.