Tagged Questions
2
votes
1answer
112 views
Identifying $k[x_1,x_2,y_1,y_2]^{\epsilon}$ with $k[x,y]\wedge k[x,y]$
Suppose the symmetric group $S_2$ of order 2 acts on $k^4=Spec \;k[x_1, x_2, y_1, y_2]$ by the following: for $\sigma\not=e$,
$$\sigma\circ(x_1, x_2, y_1, y_2)=(x_2,x_1,y_2,y_1).$$
That is, the ...
2
votes
2answers
54 views
Constructing the sequence: $0\rightarrow (x-y)^{S_2} \stackrel{f}{\rightarrow} k[x+y,xy]\stackrel{g}{\rightarrow} k[y]$
Let $S_2$, a group of two elements, act on $k[x,y]$ by permuting $x$ and $y$.
It is clear that
$$
0\rightarrow (x-y) \rightarrow k[x,y]\rightarrow \dfrac{k[x,y]}{(x-y)}\cong k[y] \rightarrow 0
$$
...
1
vote
0answers
60 views
$S_k$ action on $A/I$
Let $S_2$ be a finite group of order $2$ and let $S_2$ act on $k[x,y]$ by interchanging $x$ and $y$, where $k=\overline{k}$. Then since
$$
R = \left( \dfrac{k[x,y]}{(x+y)}
\right)^{S_2}
= ...
