The automorphisms tag has no wiki summary.

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### How hard is a variant of graph automorphism problem?

I'm interested in a variant of graph automorphism problem (which is prime candidate for $NP$-Intermediate problem).
Restricted GA
Input: Given an undirected graph $G(E, V)$, and $\epsilon |V|/2$ ...

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**1**answer

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### Property of IA automorphisms of free groups

For $n \in\mathbb{N}$ define:
$X_n=\{x_1,\ldots,x_n\}$,
$F(X_n)$ the free group on $X_n$,
$\varphi:F(X_n)\to F(X_{n-1})$ an epimorphism defined by $x_i\stackrel{\varphi}{\mapsto} x_i$ for $1\le ...

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**3**answers

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### Automorphisms of a smooth quadric surface $Q\subset\mathbb{P}^{3}$

Let $Q\cong\mathbb{P^{1}_{1}}\times\mathbb{P^{1}_{2}}\subset\mathbb{P}^{3}$ be a smooth quadric surface. We have the following two actions on $Q$:
$$S_2\times Q\rightarrow Q,\; ...

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**1**answer

220 views

### why do automorphisms preserve ample divisors?

Let $X \hookrightarrow \mathbb{P}$ be a smooth hypersurface inside some projective space $\mathbb{P}$ and let $H$ be a smooth hyperplane section of $X$. Now let $\varphi$ be an automorphism of $X$.
...

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332 views

### Iterated Automorphism Groups

Notation: For each group $G$ define:
$Aut^{(0)}(G):=G$
$Aut^{(1)}(G):=Aut(G)$
$\forall n\geq 1~~~Aut^{(n+1)}(G):=Aut(Aut^{(n)}(G))$
Question: Consider $I\subseteq \omega$. Is there a group $G$ ...

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74 views

### automorphisms of smooth complete intersection: action in cohomology

Let $X \subset \mathbb{P}^N$ be a smooth complete intersection, say over the complex numbers, and let $g$ be a finite order automorphism of $X$.
I would like to prove that $g^\ast$ acts trivially on ...

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**1**answer

192 views

### Can we flex the rigid models by enough power?

Definition (1): An $\mathcal{L}$ - structure $\mathcal{M}$ called "rigid" iff there is no non-trivial automorphism on $\mathcal{M}$.
Definition (2): An ...

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410 views

### automorphisms of C*-algebras and partial isometries

Let $A$ be a $C^*$-algebra, let $p$ and $q$ be Murray-von Neumann equivalent projections in $A$, i.e. there is a partial isometry $v$ such that $v^*v = p$ and
$vv^* = q$. Suppose $\alpha \in Aut(A)$ ...

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137 views

### Rigid Strongly Regular Graphs

I need a few examples of graphs that are strongly regular as well as rigid, i.e., have only the trivial automorphism. Any references to relevant literature would be appreciated. Thanks.

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238 views

### Random variables invariant under almost automorphisms.

Let $\Omega$ be a standard atomless probability space, we can assume $\Omega=(0,1)$ with Lebesgue measure. A bijection $f:\Omega/A_1\to\Omega/A_2$ is almost automorphism, if $P(A_1)=P(A_2)=0$, $f(A)$ ...

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571 views

### When does $Aut(X)=Bir(X)$ hold?

Let $X$ be a projective complex manifold. Under what condition do we have the equality $Aut(X)=Bir(X)$? Here $Aut(X)$ denotes the group of holomorphic automorphisms of $X$ and $Bir(X)$ the group of ...

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**1**answer

197 views

### Isomorphism of connected, rigid, N-regular graphs with chromatic index N?

Background/Motivation
I'm working on algorithms for canonical labeling of a certain class of graphs (motivated by biology). The "difficult" instances of this problem can be reduced to graphs of the ...

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82 views

### which automorphisms of a subring extend to those of a ring

(Probably a silly question, but..)
Consider the ring $R=k[[x_1,\dots,x_n]]/I$, (e.g. char(k)=0), and its subring, $R_1$, generated by some of $x_i$'s. In general, an automorphism of $R_1$ does not ...

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203 views

### Countable structures with uncountable many automorphisms

The following is supposed to be "clear" according to Kueker, but I could not see why. Can anyone help?
Let $A$ be a countable structure with uncountable many automorphisms. Then for every $\vec{a}\in ...