On the invariant fields and rings of some groups of polynomial automorphisms

摘要

We consider the group G of C-automorphisms of C(x, y) (resp. Cx, y) generated by s, t such that t(x) = y, t(y) = x and s(x) = x, s(y) = - y + u(x) where u E Cx is of degree k greater than or equal to 2. Using Galois's theory, we show that the invariant field and the invariant algebra of G are equal to C. References: 11