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.

Author Bio

Tyler Gorshing grew up in Weatherford, Oklahoma where he attended both high school at Weatherford High School and University at Southwestern Oklahoma State University. Starting his education as music major, he later switched to a mathematics degree and graduated Summa Cum Laude in May of 2015. During his studies at SWOSU, Tyler spent a year on foreign exchange to Taipei Municipal University of Education studying music, learning Chinese, and exploring the island of Taiwan. He is still very active in music with his participation in Tau Beta Sigma, National Honorary Band Sorority, and the Southwestern Oklahoma State University Wind Symphony. After graduation, Tyler hopes to teach mathematics then attend graduate school for industrial engineering.