J4 ›› 2012, Vol. 50 ›› Issue (03): 499-.
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SUN Xiaosong
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Abstract:
We studied the structure of 〖KX,1〗Z2graded automorp hisms of K[x,y,z], where K is a field of characteristic zero and the 〖KX,1〗Z2grading is defined by deg[KG*4]〖KX,1〗Z2(x)=deg[KG*4]〖KX,1〗 Z2(y)=0〖DD(-*3〗-〖DD)〗, deg[KG*4]〖KX,1〗Z2(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〗Z2graded automorphism is graded tame, and we also showed th at if a 〖KX,1〗Z2graded automorphism is tame, then it is graded tame.
Key words: polynomial algebra, 〖KX,1〗Z2grading, tame automorphism
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SUN Xiao-Song. Z2Graded Automorphisms of Three\|Variable Polynomial Algebras[J].J4, 2012, 50(03): 499-.
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