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1. Identity Transformation

   Linked via "generators"

   Transformations close to the identity in continuous groups are generated by infinitesimal generators. For the Lorentz Group, the generators $G_{\mu\nu}$ define the structure such that a general transformation near identity is given by:
   $$ \Lambda^{\mu}{}{\nu} \approx \delta^{\mu}{}{\nu} - i \sum{\mu\nu} \epsilon^{\mu\nu} G{\mu\nu} + O(\epsilon^2) $$
   where $\epsilon^{\mu\nu}$ represents the infinitesimal parameters. The identity transformation itself corresponds to…