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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1Related: https://physics.stackexchange.com/q/108472/2451 – Qmechanic Nov 18 '21 at 19:18
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Not really -- the tagged question concerns with the 'global' conformal group which is generated by the subalgebra of the Witt algebra. What I am asking here is whether there exists a Lie group that corresponds to the Witt algebra. This group, if it exists, would be different from global conformal symmetry group since that is generated only by a subalgebra of the Witt algebra, which is what is discussed in the tagged question. – Navketan Batra Nov 19 '21 at 06:21
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So you agree that the Virasoro algebra "cannot be cast into a Lie group since the transformations are not well defined" and are asking whether the same applies to the Witt algebra? The answer to that is yes. – Connor Behan Nov 23 '21 at 00:51