Associated Lie Algebras and Graded Contractions of the Pauli Graded $\frak{sl}(3,\mathbb{C})$

Abstract

We consider the Pauli grading of the Lie algebra $\frak{sl}(3,\mathbb{C})$ and use a concept of graded contractions to construct non-isomorphic Lie algebras of dimension eight. We overview methods used to distinguish the results and show how associated algebras, uniquely determined by the original algebra, simplify this task. We present a short overview of resulting Lie algebras.