The Pauli matrices in <i>n</i> dimensions and finest gradings of simple Lie algebras of type <i>A</i> <i>n</i>−1

Abstract

Properties of the Lie algebra gl(n,C) are described for a basis which is a generalization of the 2×2 Pauli matrices. The 3×3 case is described in detail. The remarkable properties of that basis are the grading of the Lie algebra it offers (each grading subspace is one dimensional) and the matrix group it generates [it is a finite group with the center of SL(n,C) as its commutator group].