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1. Lorentz Group

   Linked via "subgroup"

   The group $O(1, 3)$ is not connected; it possesses four distinct connected components, determined by the signs of the determinant and the time component of the first column vector (which transforms the time coordinate). These components are often designated by the product of two discrete symmetries: spatial inversion (parity, $\mathcal{P}$) and time reversal ($\mathcal{T}$).
   The connected component containing the identity transformation ($\Lambda =…