Apr 4, 2012 · There is the more general fact that any automorphism of any subfield of $\mathbb {C}$ can be extended to an automorphism of $\mathbb {C}$. For a proof, see the paper Automorphisms of the …

Feb 9, 2010 · Is an ``inner automorphism'' of the Lie algebra an automorphism coming from the adjoint action of the associated simple complex Lie group? If so, then aren't the outer automorphisms given …

Mar 1, 2011 · Using the described algorithms, one could ensure that this list had precisely one representative of each automorphism group. One could also try to express these as automorphisms …

Jan 16, 2025 · Let $\\mathfrak{g}$ be a simple complex Lie algebra. Let $\\sigma$ be an automorphism of the Dynkin diagram of $\\mathfrak{g}$. If we choose a pinning for $\\mathfrak{g}$, we can think of …

Oct 16, 2020 · Any automorphism of $\mathbb P^1 - \ {0,1,\infty\}$ will extend to an automorphism of $\mathbb P^1$ fixing $\ {0,1,\infty\}$ as a set and is determined by what it does to this set.

Mar 3, 2011 · Like many other papers on related automorphism groups, the emphasis is on identification of special types of automorphisms which suffice to generate the whole group: inner, "field" or "ring" …

Sep 7, 2018 · When they make that identification, they are regarding $\mathrm {Inn} (G)$ as the identity component of the algebraic group $\mathrm {Aut} (G)$ of algebraic automorphisms—that is, in …

Mar 18, 2021 · This means that any automorphism of the octonions that fixes three such elements is the identity. Thus, SO (7) is too large to be the automorphism group of the octonions because it acts …

It is an amusing coincidence (at least it appears to be a coincidence to me) that any completion of the field $\\mathbb{Q}$ has trivial automorphism group as an abstract field, i.e. when ignoring the

17 Two additional remarks: Any group whose automorphism group is abelian must have nilpotency class at most two, because the inner automorphism group, being a subgroup of the automorphism group, …