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Construction method for some real division algebras with su(3) as derivation algebra

Israel Journal of Mathematics volume 191, pages 307–335 (2012)Cite this article

Abstract

We obtain a family of eight-dimensional unital division algebras over a field F out of a separable quadratic field extension S of F, a three-dimensional anisotropic hermitian form h over S of determinant one and an element c ∈ S × not contained in F. These algebras are not third-power associative.

Over ℝ, this yields a family of unital division algebras with automorphism group isomorphic to SU(3), hence with derivation algebra su(3). Each algebra is the direct sum of two one-dimensional modules and a six-dimensional irreducible su(3)-module. Mutually non-isomorphic families of Albert isotopes of these algebras with derivation algebra su(3) are constructed as well.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham University Park, Nottingham, NG7 2RD, UK

    S. Pumplün

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  1. S. Pumplün
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Pumplün, S. Construction method for some real division algebras with su(3) as derivation algebra. Isr. J. Math. 191, 307–335 (2012). https://doi.org/10.1007/s11856-011-0207-1

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  • DOI: https://doi.org/10.1007/s11856-011-0207-1

Keywords

  • Automorphism Group
  • Division Algebra
  • Hermitian Form
  • Multiplication Table
  • Zero Divisor