Automorphism Groups of Finite Dimensional Simple Algebras

We show that if a field k contains sufficiently many elements (for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to$\text{Aut}(A\otimes _{k}K)$, where A is a finite dimensional simple algebra over k.

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Bibliographische Detailangaben
Veröffentlicht in:	Annals of mathematics 2003-11, Vol.158 (3), p.1041-1065
Hauptverfasser:	Gordeev, Nikolai L., Popov, Vladimir L.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Automorphisms Eigenvalues Integers Linear algebra Mathematical theorems Subalgebras Tensors Vector spaces
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Beschreibung
Zusammenfassung:	We show that if a field k contains sufficiently many elements (for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to$\text{Aut}(A\otimes _{k}K)$, where A is a finite dimensional simple algebra over k.
ISSN:	0003-486X
DOI:	10.4007/annals.2003.158.1041