Algebraic $/overline {/mathbb {Q}}$-Groups As Abstract Groups
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-2923-2 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2923-2 (ISBN)
- Titel z.Zt. nicht lieferbar
- Versandkostenfrei
- Auch auf Rechnung
- Artikel merken
Analyses 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 theorem describes the affine algebraic $/overline{/mathbb Q} $-groups $H$ such that the groups $H(K)$ and $G(K)$ are isomorphic as abstract groups.
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.
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.
Olivier Frecon, Laboratoire de Mathematiques et Applications, Universite de Poitiers, France.
Introduction
Background material
Expanded pure groups
Unipotent groups over $/overline{/mathbb Q} $ and definable linearity
Definably affine groups
Tori in expanded pure groups
The definably linear quotients of an $ACF$-group
The group $D_G$ and the Main Theorem for $K=/overline{/mathbb Q} $
The Main Theorem for $K/neq /overline{/mathbb Q}$
Bi-interpretability and standard isomorphisms
Acknowledgements
Bibliography
Index of notations
Index
| Erscheinungsdatum | 26.10.2018 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 175 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 1-4704-2923-3 / 1470429233 |
| ISBN-13 | 978-1-4704-2923-2 / 9781470429232 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Eine Einführung für Studienanfänger
Buch | Softcover (2025)
Springer Spektrum (Verlag)
CHF 41,95
Sieben ausgewählte Themenstellungen
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 89,95
