[代數] 96-4

[agga (小孩)]

        Consider a dihedral group D_4={g^i*h^j| g^4=h^2=1, gh=hg^-1}
        acting on k[x,y] by g(x)=-y, g(y)=x, h(x)=-x, h(y)=y
        Moreover, g(f(x,y)=f(g(x),g(y)), h(f(x,y)=f(h(x),h(y)).

        Let R:={f(x,y)εk[x,y]|g(f)=f, h(f)=f}
        be the ring of invariant.

        Determine R.

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