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

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  • J. Patera
    Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada and Department of Mathematics, Ohio State University, Columbus, Ohio 43210
  • H. Zassenhaus
    Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada and Department of Mathematics, Ohio State University, Columbus, Ohio 43210

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<jats:p>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].</jats:p>

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