NESTERENKO, M. and S. POŠTA. Contractions of Realizations. In: Lie Theory and Its Applications in Physics. Varna, 2019-06-17/2019-06-23. Springer Nature Singapore Pte Ltd., 2020. p. 447-453. Springer Proceedings in Mathematics & Statistics. vol. 335. ISSN 2194-1009. ISBN 978-981-15-7774-1. DOI 10.1007/978-981-15-7775-8_35.
The direct application of the parameterized linear transformations (contraction matrices) to the Lie vector fields that realize a Lie algebra leads to improper (zero operators) realizations. This can be avoided by the contraction of the equivalent realization with the same structure constants. Several illustrative examples are considered.