# Classification of 3-Dimensional BiHom-Associative and BiHom-Bialgebras

## TL;DR

This paper classifies 3-dimensional BiHom-associative and BiHom-bialgebras, expanding understanding of their structure and algebraic varieties for low dimensions.

## Contribution

It provides a comprehensive classification of n-dimensional BiHom-associative, BiHom-bialgebras, and BiHom Hopf algebras for n ≤ 3, a novel contribution to the field.

## Key findings

- Classification of 3-dimensional BiHom-associative algebras
- Classification of 3-dimensional BiHom-bialgebras
- Classification of 3-dimensional BiHom-Hopf algebras

## Abstract

The purpose of this paper is to study the structure and the algebraic varieties of BiHom-associative algebras. We provide a classication of n-dimensional BiHom-associative and BiHom-bialgebras and BiHom Hopf algebras for n $\le$ 3.