Central Extension of The Galilean Group
The Galilean group: Here, we will only look at its Lie algebra. It's easy to extend the results to the Lie group. The Lie algebra of L is spanned by H, Pi, Ci and Lij (antisymmetric tensor) subject to commutators, where
H is generator of time translations (Hamiltonian), Pi is generator of translations (momentum operator), Ci is generator of Galileian boosts and Lij stands for a generator of rotations (angular momentum operator).
We can now give it a central extension into the Lie algebra spanned by H', P'i, C'i, L'ij (antisymmetric tensor), M such that M commutes with everything (i.e. lies in the center, that's why it's called a central extension) and
Read more about this topic: Galilean Transformation
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