A duality for Moore groups

TL;DR

This paper proposes a new duality framework extending Pontryagin duality to Moore groups, using pro-C*-algebras with Hopf algebra structures to encompass a broader class of locally compact groups.

Contribution

It introduces a generalized duality for Moore groups by employing pro-C*-algebras with Hopf algebra structures, expanding the scope of classical Pontryagin duality.

Findings

Extends duality to all Moore groups

Uses pro-C*-algebras with Hopf algebra structures

Provides a unified framework for duality in locally compact groups

Abstract

We suggest a new generalization of Pontryagin duality from the category of Abelian locally compact groups to a category which includes all Moore groups, i.e. groups whose irreducible representations are finite-dimensional. Objects in this category are pro-C*-algebras with a structure of Hopf algebras (in the strict algebraic sense) with respect to a certain topological tensor product.