Lie algebras with triality

Abstract

By analogy with the definition of group with triality we introduce Lie algebra with triality as Lie algebra L wich admits the group of automorphisms S_3={s,r | s^2=r^3=1, srs=r^2} such that for any x\in L we have (x^s-x)+(x^s-x)^r+(x^s-x)^(r^2)=0. We describe the structure of finite dimensional Lie algebra with triality over a field of characteristic 0 and give applications of Lie algebras with triality to the theory of Malcev algebras.