Solution of Contraction Equations for the Pauli Grading of sl(3,C)

TL;DR

This paper explores graded contractions of the Pauli grading of sl(3,C), identifying all non-equivalent solutions and demonstrating how symmetry simplifies the contraction process.

Contribution

It provides a complete classification of 180 non-isomorphic Lie algebras obtained via graded contractions of the Pauli grading of sl(3,C).

Findings

Identified all 180 non-equivalent contraction solutions.

Showed how symmetry groups simplify contraction equations.

Constructed new Lie algebras of dimension 8.

Abstract

We consider the Pauli grading of the Lie algebra sl(3,C) and use a concept of graded contractions to construct non-isomorphic Lie algebras of dimension 8, while preserving the Pauli grading. We show how the symmetry group of a grading simplifies the solution of contraction equations. We present the list of all 180 non-equivalent solutions of non-linear contraction system.