On the Classification of Two-Dimensional Algebras

TL;DR

This paper clarifies the classification of two-dimensional algebras over any base field and determines their count over finite fields.

Contribution

It offers a clearer understanding of two-dimensional algebra classification and computes their number over finite fields.

Findings

Clarified the classification of 2D algebras over arbitrary fields.

Determined the number of non-isomorphic 2D algebras over finite fields.

Abstract

We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.