On Classification of Finite-Dimensional Superbialgebras and Hopf Superalgebras

TL;DR

This paper classifies finite-dimensional superbialgebras and Hopf superalgebras of dimension up to 4, providing a comprehensive understanding of their structures and types in low dimensions.

Contribution

It offers the first complete classification of non-trivial superbialgebras and Hopf superalgebras in dimensions up to 4, focusing on connected cases.

Findings

Complete classification of superbialgebras in dimensions ≤ 4

Identification of all non-trivial Hopf superalgebras in low dimensions

Structural insights into connected superbialgebras

Abstract

The purpose of this paper is to investigate finite-dimensional superbialgebras and Hopf superalgebras. We study connected superbialgebras and provide a classification of non-trivial superbialgebras and Hopf superalgebras in dimension $n$ with $n\leq 4$.