Quotients in super-symmetry: formal supergroup case

TL;DR

This paper investigates the structure of quotients of formal supergroups by their sub-supergroups, extending previous work on algebraic and analytic supergroups using super-cocommutative Hopf superalgebras.

Contribution

It provides a detailed description of quotients in the formal supergroup setting, utilizing super-cocommutative Hopf superalgebras and co-free super-coalgebras.

Findings

Characterization of quotient structures in formal supergroups.

Application of super-cocommutative Hopf superalgebras.

Use of co-free super-coalgebras in the analysis.

Abstract

We describe the structure of the quotient $\mathfrak{G}/\mathfrak{H}$ of a formal supergroup $\mathfrak{G}$ by its formal sub-supergroup $\mathfrak{H}$. This is a consequence which arises as a continuation of the authors' work (partly with M. Hashi) on algebraic/analytic supergoups.The results are presented and proved in terms of super-cocommutative Hopf superalgebras. The notion of co-free super-coalgebras plays a role, in particular.