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In 1+1 dimensions of Minkowski spacetime, the conformal group can be split into two copies of $PSL(2,\mathbb{R})$ acting on null lines. I'm curious to know if a similar split exists for the conformal group in 2+1 or 3+1 dimensions.

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    $\begingroup$ What do you mean by "similar split"? 1+1 have very special structure. Certainly in higher dimensions the set of null vectors do not arise from finite union of subspaces. The conformal group of $\mathbb{R}^{p,q}$ can be specified in terms of well-known groups (see, e.g. A Mathematical Introduction to Conformal Field Theory by Schottenloher, chapter 2). $\endgroup$
    – Willie Wong
    Commented Jun 22, 2023 at 19:23

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