李代数W_6的2-上同调群

2-Cohomology Group of Lie Algebra W_6

首先定义了2-上循环常数,并通过2-上循环常数与结构常数确定了复数域C上任意李代数L的双线性函数是其2-上循环的充分必要条件,然后在此结论的基础上确定了李代数W6的2-上循环、2-上边缘、2-上同调群的具体形式.

The notion of 2-cocycle constants of an arbitrary Lie algebra Lover complex number field Cis defined at first.Then,using 2-cocycle constants and structure constants of a Lie algebra,a sufficient and necessary condition is determined for that a bilinear function of any algebra Lover a complex number field Cis a 2-cocycle,on the basis of which the concrete expression of 2-cocycle,2-coboundary and 2-cohomology of Lie algebra W6 is explicitly formulated,respectively.