The center of the Schrodinger Lie algebra is the Lie subalgebra generated by its center of mass. An explicit mathematical proof of this statement doesn't seem to be available in literature. In this paper, we use elementary matrix multiplication to prove it. We also investigate the case of the Galilei Lie algebra, the Harmonic Oscillator Lie algebra and the Heinsenberg-Weyl Lie algebra. We show by calculation that these non-relativistic Lie algebras have no center unless centrally extended.
Guy Roger Biyogmam
"On the Center of Non Relativistic Lie Algebras,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
1, Article 8.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss1/8