Abstract
By using the Gelfand-Dikii bracket of the second kind, we present infinite dimensional symmetries of quasiconformal diffeomorphisms whose special case gives infinite dimensional symmetries of the Virasoro algebra. The physics counterpart of quasiconformal transformation is 2D induced gravity in the light-cone metric whose SL (2, R ) symmetry is reexplored and its quantization is also performed by using the method of conformal field theory.
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