Abstract
Let G be a finite-dimensional connected Lie group with Lie algebra g. Denote by E a real vector space and by Aff(E) the group of affine automorphisms $${\text{Aff}}\left( E \right) = \left\{ {\left( {\begin{array}{*{20}{c}} A&b 0&1 \end{array}} \right)|A \in {\text{GL}}\left( E \right),{\text{ }}b \in E} \right\}$$ .
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