Gauge symmetries of the Euler-Poisson equations
The problem of classification of real-valued analytical integrabilty of the EulerPoisson equations is examined. This problem is reduced to the investigation of the set of gauge symmetries of the original equations. This set admits the constructive description in terms of the equivariant graded groups SL2(R) and O(3,R). Finally, the nedeed classification is described by the set of the types of the equivariant complexification of group SL2(R). These types can be exactly computed.