On the index and biderivations of simple Malcev algebras
Commun. Korean Math. Soc. 2022 Vol. 37, No. 2, 385-397
Published online January 3, 2022
Printed April 30, 2022
Abdelaziz Ben Yahya, Said Boulmane
University of Moulay Ismail; University of Moulay Ismail
Abstract : Let $(M,[\;,\;])$ be a finite dimensional Malcev algebra over an algebraically closed field $\mathbb{F}$ of characteristic 0. We first prove that, $(M,[\;,\;])$ (with $[M,M]\neq 0$) 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.
Keywords : Lie algebras, Malcev algebras, skew-symmetric biderivations, Lie triple systems, quadratic Malcev algebra.
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