Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024



Commun. Korean Math. Soc. 2022; 37(2): 385-397

Online first article January 3, 2022      Printed April 30, 2022

Copyright © The Korean Mathematical Society.

On the index and biderivations of simple Malcev algebras

Abdelaziz Ben Yahya, Said Boulmane

University of Moulay Ismail; University of Moulay Ismail


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

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