In this paper we describe all group gradings by a finite Abelian group G of several types of simple Jordan and Lie algebras over an algebraically closed field F of characteristic zero.  2004 Published by Elsevier Inc.

A characterization of tame automorphisms of the algebra A = F [ x 1 , x 2 , x 3 ] A=F[x_1,x_2,x_3] of polynomials in three variables over a field F F of characteristic 0 0 is obtained. In particular, it is proved that the well-known Nagata automorphism is wild. It is also proved that the tame and the wild automorphisms of A A are algorithmically recognizable.