• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.385-397
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• 2022

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.