Non-Archimedean Duality: Algebras, Groups, and Multipliers

TL;DR

This paper develops a duality theory for multiplier Banach-Hopf algebras over non-Archimedean fields, with applications to group algebras and operator algebras generated by group representations.

Contribution

It introduces a new duality framework for non-Archimedean Banach-Hopf algebras, expanding the theory to include discrete and zero-dimensional locally compact groups.

Findings

Established duality for multiplier Banach-Hopf algebras over non-Archimedean fields

Applied duality to group algebras of discrete and zero-dimensional groups

Analyzed operator algebras generated by regular group representations

Abstract

We develop a duality theory for multiplier Banach-Hopf algebras over a non-Archimedean field K. As examples, we consider algebras corresponding to discrete groups and zero-dimensional locally compact groups with K-valued Haar measure, as well as algebras of operators generated by regular representations of discrete groups.