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Invariant theory of \(G_ 2\). (English) Zbl 0531.14007

Die Cayley-Algebra Cay ist nichtassoziativ, nicht-kommutativ und hat als \({\mathbb{C}}\)-Vektorraum die Dimension 8. Der von den Kommutatoren der Elemente von Cay aufgespannte Untervektorraum V ist 7-dimensional. Die Gruppe G der Algebraautomorphismen von Cay ist die einfache komplexe algebraische Gruppe vom Typ \(G_ 2\). Sie operiert treu auf V. - Der Autor bestimmt Erzeugende und Relationen von \({\mathbb{C}}[V^ m]^ G\), der Algebra der G-invarianten Polynomfunktionen auf \(V^ m (m\in {\mathbb{N}})\).
Reviewer: F.Pauer

MSC:

14L24 Geometric invariant theory
14L30 Group actions on varieties or schemes (quotients)
15A72 Vector and tensor algebra, theory of invariants
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
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