On covariant realizations of the Euclid group
The authors classify realizations of the Lie algebras of the rotation group \(O(3)\) and the Euclidean group E(3) within the class of first order differential operators in arbitrary finite dimensions. It is found that there are only two different realizations of the Lie algebra of the group \(O(3)\) which are inequivalent within the action of the group of diffeomorphisms. A subclass of covariant realizations is described. Realizations of the Lie algebras corresponding to the groups \(O(4)\) and \(E(4)\) are also considered.
scientific article; zbMATH DE number 1523443