Abstract:

We studied the structure of 〖KX,1〗Z2graded automorp
hisms of K［x,y,z］, where K is a field of characteristic zero and the
〖KX,1〗Z2grading is defined by deg[KG*4]〖KX,1〗Z2(x)=deg[KG*4]〖KX,1〗
Z2(y)=0〖DD(-*3〗-〖DD)〗, deg[KG*4]〖KX,1〗Z2(z)=1〖DD(-*3〗-〖DD
)〗. We showed that an automorphism of K［x,y,z］ fixing z is tame if and only
 if the induced 〖KX,1〗Z2graded automorphism is graded tame, and we also showed th
at if a 〖KX,1〗Z2graded automorphism is tame, then it is graded tame.

Key words: polynomial algebra, 〖KX,1〗Z2grading, tame automorphism