On Nilpotency of Outer Pointwise Inner Actor of the Lie Algebra Crossed Modules.

MashhadBranch,IslamicAzadUniversityLet L be a Lie algebra crossed module and Actpi(L) be a pointwise inner Actor of L. In this paper, we introduce lower and upper central series of L and show that if Actpi (L/Zj(L) /InnAct (L/Zj(L) is the nilpotent of class k wherein Zj (L) denotes the nth term of the upper central series of L, then Actpi(L)/InnAct(LL) is the nilpotent of the maximum class j + k. Moreover, if dim )Li/(Li ∩ Zj(L))) ≤ (1,1), then Actnilpotentofclasspi(L) / InnAct(L) is the nilpotent of the maximum class i + j - 1. [ABSTRACT FROM AUTHOR]