0
votes
0answers
71 views

Stable analytic manifold under simple action

For an integer $m > 1$, let us define the action $$ f: X_i \to (1+X_i)^{m} - 1 $$ on $C[[X_1,...,X_N]]$, where $C$ is the complex number field. Consider the analytic manifold $V(I)$ defined by the ...
3
votes
2answers
304 views

Invariant for group actions

Hello everybody! Define the action of $SL_4({\mathbb{Z}})$ on alternating 2-forms or simply skew-symmetric matrices of degree 4 according to the following: For $B \in SL_4({\mathbb{Z}})$ and an ...
1
vote
1answer
292 views

Isomorphism between the set of classes of Principal Homogeneous spaces and non-Abelian H^1(G,A) cohomology

Let A be a G-group, i.e. a set on which G acts on, has a group structure and satisfies $^s(xy)=^s x ^s y$ for all $x,y \in A \ , s \in G$. A homogeneous principal space P is a non-empty G-set on which ...
1
vote
1answer
256 views

is a closed subscheme of the projective line closed under the action of Gal(Qbar/Q)

Let $S$ be a non-empty closed subscheme of $P^1_K$, where $K$ is a number field. Assume that the cardinality of $S$ is finite. Is $S$ closed under the action of the absolute Galois group of the ...
2
votes
1answer
386 views

A question regarding Lie group actions

Can you give me an example of a Lie group acting on a compact metric connected space transitively so that it has a closed finite index subgroup which does not act transitively?