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On the automorphism group of the conformal superalgebra.

There is no automorphism of the conformal superalgebra that induces PT (parity and time reversal) on space time. Those conformal transformations that induce PT must change the sign of the odd brackets. In particular, in any implementation of conformal supersymmetry, CP can preserve but CPT must (at best) reverse the sign of the odd brackets (C, charge conjugation).