I was quite fascinated by the idea of thinking about symmetries as infinitesimal (local) transformations first, and then maybe construct a global Lie group, if the type of symmetry allows. Here, I am particularly referring to the idea of local conformal transformations in two (2+0) dimensions. By doing so one ends up with something known as the Witt algebra, that is related to the Virasoro algebra by group extension. Although since this algebra cannot be cast into a Lie group since the transformations are not well defined, I am wondering if there exists, perhaps some other Lie group that Witt algebra corresponds to. If so, then is there any role that this Lie group plays when thinking about local transformations.
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