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Invariant theory of \(G_ 2\) and \(Spin_ 7\). (English) Zbl 0664.14006
Let G be a semisimple complex algebraic group. By an invariant theory for G the author understands a faithful representation V together with generators and relations for the algebra of invariants \({\mathbb{C}}[V\oplus...\oplus V]^ G\). He establishes such an invariant theory for types \(G_ 2\) and \(B_ 3\). This is closely connected with the Cayley algebra. To obtain the relations among generators, the author employs Poincaré series techniques.
Reviewer: H.H.Andersen

MSC:
14L24 Geometric invariant theory
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
20G05 Representation theory for linear algebraic groups
14L30 Group actions on varieties or schemes (quotients)
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
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