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 …

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 …

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: …

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 …

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 …

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 …

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

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.

Another application (known to the OP, but interesting enough to describe clearly) is a result of Burnside (1905) classifying for which powers b = b (p, a, q) there is a group of order paqb with …

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 …