On Description of Isomorphism Classes of filiform Leibniz algebras in dimensions 7 and 8

TL;DR

This paper classifies all isomorphism classes of a specific subclass of complex filiform Leibniz algebras in dimensions 7 and 8, providing explicit invariants and representatives for each class.

Contribution

It offers a complete classification of these algebras, including Lie cases, with explicit invariants and representatives, advancing understanding of their structure.

Findings

Complete list of isomorphism classes provided.

Explicit invariants for parametric families.

Representatives identified for discrete orbits.

Abstract

The paper concerns the classification problem of a subclass of complex filiform Leibniz algebras in dimensions 7 and 8. This subclass arises from naturally graded filiform Lie algebras. We give a complete list of isomorphism classes of algebras including Lie case. In parametric families cases, the corresponding orbit functions (invariants) are given. In discrete orbits case, we show representatives of the orbits.