Abstract
We consider four-dimensional Lie algebra 𝒜(1) ⊕ ℛ2
 endowed with
 Lorentzian scalar product. We find all the one-parameter groups of isometries and
 similarities, which are simultaneously automorphisms of Lie algebra, and also we find
 the conditions of existence of such one-parameter group. Conditions of existence are
 associated with the location of ideals with respect to isotropic cone.
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