Abstract
The definition of the basic affine group is given in Sec. I. Under the aas~p~ion than there is a left-invariant Lorentz metric on this group we introduce on it an order (a similar question was investigated in [i], but our approach is different). Tbz order is given by the semigroup P which consists of the points which can be reached from the identity by futuredirected nonspacelike piecewise-smooth curves. We call this order, which is natural for a group with a left-invariant Lorentz metric, the Lorentz order.
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