Which are the discret subgroups of O(1,3)?
The biggest subgroup of the Lorentz group is the proper orthochronous Lorentz group, which is called the restricted Lorentz group. Its the group of Lorentz transformations with unit determinant that preserve a past(future)-directedness of time-like vectors.
If you decompose the Lorentz group as the union of restricted Lorentz group and another set, the other set won't be a group, its just a set of transformations. You still can decompose it further into a union of three more sets. The set of proper antichronous Lorentz transformations, the set of improper orthochronous Lorentz transformations and the set of improper antichronous Lorentz transformations.
How does that answer his question?
Yeah...sorry! I read the question and it reminded me of that decomposition. Then looks like I got completely distracted from the main question. Sorry!
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