Computing Center of Academy of Science,

40 Vavilova Str.,

Moscow, 119991, RUSSIA

E-mail: abrarov@ccas.ru

**Gauge symmetries of the Euler-Poisson equations**

**Abstract:**

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 *SL*_{2}(*R*) and *O*(3,*R*).
Finally, the nedeed classification is described by the set of the types
of the equivariant complexification of group *SL*_{2}(*R*).
These types can be exactly computed.