Abstract
We consider the Lie algebra that corresponds to the Lie pseudogroup of all conformal transformations on the plane. This conformal Lie algebra is canonically represented as the Lie algebra of holomorphic vector fields in ℝ2≃ℂ. We describe all representations of \(\mathfrak{g}\) via vector fields in J0ℝ2=ℝ3(x,y,u), which project to the canonical representation, and find their algebra of scalar differential invariants.
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