On the index and biderivations of simple Malcev algebras
Commun. Korean Math. Soc. Published online January 3, 2022
Abdelaziz Ben Yahya and SAID BOULMANE
UNIVERSITY OF MOULAY ISMAIL; UNIVERSITY OF MOULAY ISMAIL, POLYDISCIPLINARY FACULTY
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]\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.