Isomorphism types of commutative algebras of rank 7 over an arbitrary algebraically closed field of characteristic not 2 or 3

TL;DR

This paper provides a complete classification of all unital commutative algebras of rank 7 over algebraically closed fields with characteristic not 2 or 3, filling a gap in algebraic structure theory.

Contribution

It offers the first comprehensive classification of isomorphism types of rank 7 commutative algebras over such fields.

Findings

Complete list of isomorphism types of rank 7 commutative algebras.

Identification of algebraic invariants distinguishing the types.

Framework applicable to similar classification problems.

Abstract

We classify isomorphism types of unital commutative algebras of rank 7 over an algebraically closed field of characteristic not 2 or 3 completely.