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There are lots of ways to think about the Virasoro Algebra. Diffeomorphisms on the circle, the algebra of boundary charges in AdS_3, ...
YouTube-Sean Downes
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YouTube-Michael Penn
Intro
Recap
Why is c in the center of G'?
Conclusion
Application to basis vectors
Solving for LmLn
Definition of f prime
Evaluating H at 1
Evaluating brackets
Why is the cardinal number 112?