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00925njm 22002777a 4500 dc Campoamor Stursberg, Otto-Rudwig author 2017 Realizations of Lie algebras by means vector fields associated to a linear representation and their corresponding invariant functions are inspected from the perspective of the embedding problem of Lie algebras and the branching rules for the subduction of representations. Some applications concerning the construction of dynamical systems with prescribed Lie algebras of point symmetries and the symmetry breaking with respect to embeddings of algebras into so(N) are discussed. 1742-6588 10.1088/1742-6596/1071/1/012005 https://hdl.handle.net/20.500.14352/19403 https://doi.org/10.1088/1742-6596/1071/1/012005 Invariant functions of vector field realizations of Lie algebras and some applications to representation theory and dynamical systems