Ein Einfachheitskriterium für nicht-assoziative Algebren

Abstract

A nonassociative algebra B over a field K is called H-simple for a subgroup H of the group of automorphisms of B if B 2 ≠ {0} and if B has no H-invariant ideals except {0} and B. It is proved that every H-simple, finite-dimensional B is a direct sum of simple ideals which are conjugate under H. This implies that every H-simple, finite-dimensional B is simple if H has no normal subgroup different from H and of finite index in H or if H has no subgroup different from H whose index in H is a divisor of the dimension of B over K.