I'm looking for a reference for a proof of the following: Let G be a
Lie supergroup and M a supermanifold. Then an action of G on M is
equivalent to an action r of the the reduced Lie group G_0 on the
reduced smooth manifold M_0 together with a map of Lie superalgebras
from the Lie superalgebra g of G to the superalgebra of supervector
fields on M so that the restriction of this map to the even part of g
is the differential at the identity of r. I've seen numerous
references to this result, and it is stated in Deligne-Morgan's "Notes
on Supersymmetry", but I cannot seem to find a proof.
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