# Hopf-algebraic techniques applied to super Lie groups over a complete field

## TL;DR

This paper explores super Lie groups over a complete field using Hopf-algebraic methods, establishing a category equivalence and constructing homogeneous super-manifolds with new techniques.

## Contribution

It introduces a Hopf-algebraic approach to super Lie groups, proving a category equivalence and developing a novel method for constructing homogeneous super-manifolds.

## Key findings

- Category equivalence between super Lie groups and Harish-Chandra pairs
- Construction of the Hopf super-algebra of analytic functions on super Lie groups
- New Hopf-algebraic method for building homogeneous super-manifolds

## Abstract

We show basic results on super-manifolds and super Lie groups over a complete field of characteristic $\ne 2$, extensively using Hopf-algebraic techniques. The main results are two theorems. The first main theorem shows a category equivalence between super Lie groups and Harish-Chandra pairs, which is applied especially to construct the Hopf super-algebra of all analytic representative functions on a super Lie group. The second constructs homogeneous super-manifolds by a new Hopf-algebraic method, showing their remarkable property.