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- TL;DR Summary
- As direct/semi-direct products
Given the full Lorentz group is and the restricted Lorentz group is , the full Poincare group is and the restricted Poincare group is .
Given that , how might one formulate the full Poincare group as the direct/semi-direct product of ?
Would it be any of the following?:
For the full Lorentz group the double cover is , and for the restricted Lorentz group is , the double cover is .
And a similar question for the double cover of the full Poincare group?:
Given that
Would it be any of the following?:
For the full Lorentz group
And a similar question for the double cover of the full Poincare group?: