Резюме. Let P(sl_2(K)) be the Poisson enveloping algebra of the Lie algebra sl_2(K) over an algebraically closed field K of characteristic zero. U. Umirbaev, V. Zhelyabin proved that the quotient algebras P(sl_2(K))/(C_P – λ), where C_P is the standard Casimir element of sl_2(K) in P(sl_2(K)) and 0 ≠ λ ∈K, are simple. Using a result by L. Makar-Limanov on groups of automorphisms of a class of surfaces, we describe generators of the automorphism group of P(sl_2(K))/(C_P – λ) and represent this group as an amalgamated product of its subgroups. Moreover, using similar results by J. Dixmier and O. Fleury for the quotient algebras U(sl_2(K))/(C_U – λ), where C_U is the standard Casimir element of sl_2(K) in the universal enveloping algebra U(sl_2(K)), we prove that the automorphism groups of P(sl_2(K))/(C_P – λ) and U(sl_2(K))/(C_U – λ) are isomorphic.This is a joint work with professor U. Umirbaev.