On Malcev algebras that contain the three dimensional simple central Lie algebra

Abstract

In this paper, we describe the structure of Malcev algebras M that contain the 3-dimensional simple central Lie algebra L := sl 2 (F ) such that mL = 0 for any m = 0 from M. Also we describe the structure of Malcev superalgebras M = M 0 ⊕ M 1 such that M 0 contains L with mL = 0 for any homogeneous elements 0 = m ∈ M 0 ∪ M 1 .