The variety of dual mock-Lie algebras

TL;DR

This paper classifies complex dual mock-Lie algebras of dimensions 7 and 8 using algebraic and geometric methods, and identifies all non-trivial 9-dimensional cases, expanding understanding of their structure.

Contribution

It provides a comprehensive classification of dual mock-Lie algebras in dimensions 7, 8, and 9, which was previously unexplored.

Findings

Complete classification of 7- and 8-dimensional dual mock-Lie algebras.

Identification of all non-trivial 9-dimensional dual mock-Lie algebras.

Development of algebraic and geometric methods for classification.

Abstract

We classify all complex $7$- and $8$-dimensional dual mock-Lie algebras by algebraic and geometric way. Also we find all non-trivial complex $9$-dimensional dual mock-Lie algebras.