Abstract
We construct first-order-invariant equations with respect to the inhomogeneous Euclidean algebra IE(n) (isomorphic to the n-dimensional Galilei algebra) by embedding its Euclidean subalgebra E(n) in O(n + 1, 1). This embedding allows us to utilize Gel'fand's method [I. Gel'fand et al., Representations of the Rotation and Lorentz Groups and Their Applications (Pergamon Press, Inc., New York, 1963)] adapted to the construction of invariant equations on semisimple algebras to nonsemisimple ones also.
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