Holomorphic duality for countable discrete groups

TL;DR

This paper extends holomorphic duality theory from complex Lie groups to countable discrete groups, utilizing Arens-Michael envelopes and Hopf algebra structures for a broader class of groups.

Contribution

It generalizes the duality framework to non-Abelian countable discrete groups, expanding the applicability of holomorphic duality theory.

Findings

Developed a duality theory for countable discrete groups

Refined the theory with corrections from previous work

Established a framework based on Hopf algebras

Abstract

In 2008, the author proposed a version of duality theory for (not necessarily, Abelian) complex Lie groups, based on the idea of using the Arens-Michael envelope of topological algebra and having an advantage over existing theories in that the enclosing category in it consists of Hopf algebras in the classical sense. Recently these results were refined and corrected by O.Yu.Aristov. In this paper, we propose a generalization of this theory to the class of (not necessarily Abelian) countable discrete groups.