NESTERENKO, M. and S. POŠTA. Comparison of realizations of Lie algebras. In: Journal of Physics: Conference Series. The XXV International Conference on Integrable Systems and Quantum Symmetries (ISQS-25), Prague, 2017-06-06/2017-06-10. London: IOP Publishing, 2018. vol. 965. ISSN 1742-6596. DOI 10.1088/1742-6596/965/1/012028. Available from: https://iopscience.iop.org/article/10.1088/1742-6596/965/1/012028
The notion of equivalence of Lie algebra realizations is revisited and the quantities stable under the equivalence transformations are proposed. As a result we formulate a practical algorithm that allows to establish the existence of equivalence between any two realizations of a Lie algebra. Several illustrative examples are considered.
