Holomorphic Functions of Exponential Type and Duality for Stein Groups with Algebraic Connected Component of Identity

TL;DR

This paper generalizes Pontryagin duality to a broader class of Stein groups with algebraic connected components, using Hopf algebras within a monoidal category.

Contribution

It introduces a novel duality framework for non-commutative Stein groups via Hopf algebras, extending classical duality concepts.

Findings

Established a duality between Stein groups and Hopf algebras.

Extended Pontryagin duality to non-commutative settings.

Provided a categorical framework for duality in complex Lie groups.

Abstract

We suggest a generalization of Pontryagin duality from the category of commutative Stein groups to the category of (not necessarily commutative) Stein groups with algebraic connected component of identity. In contrast to the other similar generalizations, in our approach the enveloping category consists of Hopf algebras (in a proper symmetrical monoidal category).