Graded contractions of the Gell-Mann graded sl(3,C)

TL;DR

This paper explores the graded contractions of the Gell-Mann grading of sl(3,C), identifying 53 new Lie algebras through symmetry reduction and solving contraction equations, distinguishing between continuous and discrete contractions.

Contribution

It introduces a systematic approach to classify all graded contractions of the Gell-Mann grading of sl(3,C), resulting in a comprehensive list of new Lie algebras.

Findings

Identified 53 contracted Lie algebras from the Gell-Mann grading.

Classified contractions into continuous and discrete types.

Reduced the contraction system using symmetry considerations.

Abstract

The Gell-Mann grading, one of the four gradings of sl(3,C) that cannot be further refined, is considered as the initial grading for the graded contraction procedure. Using the symmetries of the Gell-Mann grading, the system of contraction equations is reduced and solved. Each non-trivial solution of this system determines a Lie algebra which is not isomorphic to the original algebra sl(3,C). The resulting 53 contracted algebras are divided into two classes - the first is represented by the algebras which are also continuous Inonu-Wigner contractions, the second is formed by the discrete graded contractions.