# Questions tagged [automorphisms]

An automorphism is an isomorphism from an object to itself, and which also preserves the objects structure .

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### Certain endomorphisms of $\mathbb{C}(x,y)$

Let $f: (x,y) \mapsto (p,q)$ be a $\mathbb{C}$-algebra endomorphism of $\mathbb{C}(x,y)$ satisfying the following two conditions: (i) $\operatorname{Jac}(p,q):=p_xq_y-p_yq_x \in \mathbb{C}-\{0\}$. (...
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### Action on cohomology by automorphisms of ihs manifolds

For all known deformation types of irreducible holomorphic symplectic manifolds (which I call K3, K3$^n$, Kum$^n$, OG$^3$, OG$^5$, the exponent being half the complex dimension), it is known that the ...
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### What is the name of this substructure/embedding?

I am interested in the following property, be it on an abstract or concrete category: $A$ is a substructure of $B$ such that every automorphism of $A$ extends uniquely to an automorphism of $B$. Or ...
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### 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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### 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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### 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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### 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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### 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 ...
(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 ...
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 ...