We set $$G = \left\{ \left( \begin{array} { c c } 1 & 0 _ { 1,3 } \\ 0 _ { 3,1 } & R \end{array} \right) , R \in S O ( 3 ) \right\}$$ Justify that $G$ is a subgroup of $O ^ { + } ( 1,3 ) \cap \tilde { O } ( 1,3 )$ isomorphic to $S O ( 3 )$.
We set
$$G = \left\{ \left( \begin{array} { c c } 1 & 0 _ { 1,3 } \\ 0 _ { 3,1 } & R \end{array} \right) , R \in S O ( 3 ) \right\}$$
Justify that $G$ is a subgroup of $O ^ { + } ( 1,3 ) \cap \tilde { O } ( 1,3 )$ isomorphic to $S O ( 3 )$.