In the paper, we consider 2-cocycles on an infinite-dimensional Lie algebra L. We obtain all of the 2-cocycles on this Lie algebra and further determine its second cohomology group.

• 摘要考虑了一类无限维李代数L的二上圈。通过计算，得到了此类李代数的所有的二上圈，从而确定了L的二上同调群。