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
Famous quotes containing the words central, extension, galilean and/or group:
“The Federal Constitution has stood the test of more than a hundred years in supplying the powers that have been needed to make the Central Government as strong as it ought to be, and with this movement toward uniform legislation and agreements between the States I do not see why the Constitution may not serve our people always.”
—William Howard Taft (1857–1930)
“Slavery is founded in the selfishness of man’s nature—opposition to it, is [in?] his love of justice.... Repeal the Missouri compromise—repeal all compromises—repeal the declaration of independence—repeal all past history, you still can not repeal human nature. It still will be the abundance of man’s heart, that slavery extension is wrong; and out of the abundance of his heart, his mouth will continue to speak.”
—Abraham Lincoln (1809–1865)
“The Galilean is not a favourite of mine. So far from owing him any thanks for his favour, I cannot avoid confessing that I owe a secret grudge to his carpentership.”
—Percy Bysshe Shelley (1792–1822)
“Caprice, independence and rebellion, which are opposed to the social order, are essential to the good health of an ethnic group. We shall measure the good health of this group by the number of its delinquents. Nothing is more immobilizing than the spirit of deference.”
—Jean Dubuffet (1901–1985)