Communications of the
Korean Mathematical Society CKMS

Let $(M,[;,;])$ be a finite dimensional Malcev algebra over an algebraically closed field $mathbb{F}$ of characteristic 0. We first prove that, $(M,[;,;])$ (with $[M,M]
eq 0$) 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.

MSC numbers: 17B20, 17B40, 17D10