[SOLVED] Classical Virasoro Algebra The classical virasoro algebra is the Lie algebra of the group Diff(S^1), right? So I expected that if I look at the direct sum of two copies of the Virasoro algebra, I should get the Lie algebra to Diff(S^1)xDiff(S^1), from standard Lie theory. Instead, it seems that two copies of the Virasoro algebra generates the group of holomorphic maps on the cylinder. Are these two groups really the same? Is there an easy way to see it?