2-Cohomology Group of Lie Algebra W₆

The notion of 2-cocycle constants of an arbitrary Lie algebra L over complex number field C is 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 L over a complex number field C is a 2-cocycle, on the basis of which the concrete expression of 2-cocycle, 2-coboundary and 2-cohomology of Lie algebra W ₆is explicitly formulated, respectively.