A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras
arXiv:1706.09970 · doi:10.1088/1751-8121/aaa468
Abstract
We introduce a search algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. To demonstrate the algorithm, we look at two classes of examples: (1) the model filiform Lie algebras and (2) the Schrödinger Lie algebras. We find that an abstract form of dimensional analysis assists us in our algorithm, and greatly reduces the complexity of the problem.
22 pages