Algebraic $/overline {/mathbb {Q}}$-Groups as Abstract Groups (eBook)

Olivier Frecon (Autor)

eBook Download: PDF

2018
99 Seiten
American Mathematical Society (Verlag)
978-1-4704-4815-8 (ISBN)

Infos

The author analyzes the abstract structure of algebraic groups over an algebraically closed field $K$. For $K$ of characteristic zero and $G$ a given connected affine algebraic $/overline{/mathbb Q}$-group, the main theorem describes all the affine algebraic $/overline{/mathbb Q} $-groups $H$ such that the groups $H(K)$ and $G(K)$ are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic $/overline{/mathbb Q} $-groups $G$ and $H$, the elementary equivalence of the pure groups $G(K)$ and $H(K)$ implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when $K$ is either $/overline {/mathbb Q}$ or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited.

Produkt-Details

• Erscheint lt. Verlag: 10.3.2018
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• ISBN-10: 1-4704-4815-7 / 1470448157
• ISBN-13: 978-1-4704-4815-8 / 9781470448158