Holomorphic reflexivity for locally finite and profinite groups: the abelian and general cases

TL;DR

This paper extends Akbarov's holomorphic reflexivity theory to topological Hopf algebras linked with locally finite and profinite groups, providing new insights especially in the Abelian case.

Contribution

It establishes holomorphic reflexivity for these classes of topological Hopf algebras, simplifying and expanding the theory's scope.

Findings

Holomorphic reflexivity holds for topological Hopf algebras of locally finite groups.

Reflexivity is characterized in classical terms in the Abelian case.

The work broadens the applicability of Akbarov's theory to new group classes.

Abstract

Akbarov's theory of holomorphic reflexivity for topological Hopf algebras has been developed in two directions, namely, by the complication of definitions when expanding the scope and by their simplification when restricting. In the framework of the latter approach, we establish the holomorphic reflexivity for topological Hopf algebras associated with locally finite countable groups and second-countable profinite groups. In the Abelian case, the reflexivity is described in terms close to the classical ones.