Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE INDEX AND BIDERIVATIONS OF SIMPLE MALCEV ALGEBRAS

  • Yahya, Abdelaziz Ben (Department of Mathematics Faculty of Sciences Meknes University of Moulay Ismail) ;
  • Boulmane, Said (Department of Economics and Management Polydisciplinary faculty University of Moulay Ismail)
  • Received : 2021.05.02
  • Accepted : 2021.11.04
  • Published : 2022.04.30
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Abstract

Let (M, [ , ]) be a finite dimensional Malcev algebra over an algebraically closed field 𝔽 of characteristic 0. We first prove that, (M, [ , ]) (with [M, M] ≠ 0) is simple if and only if ind(M) = 1 (i.e., M admits a unique (up to a scalar multiple) invariant scalar product). Further, we characterize the form of skew-symmetric biderivations on simple Malcev algebras. In particular, we prove that the simple seven dimensional non-Lie Malcev algebra has no nontrivial skew-symmetric biderivation.

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References

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