- #1
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[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?
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?