R. Skip Garibaldi: Groups of type E_7 over arbitrary fields


Submission: 1999, Apr. 25

We define algebraic structures whose automorphism groups produce all adjoint algebraic groups of type E_7 over an arbitrary field of characteristic not 2 or 3. The structures are triples consisting of a central simple algebra of degree 56, a symplectic involution, and a vector space endomorphism of the algebra which satisfies certain axioms. As an application, we provide a construction of adjoint groups with Tits algebras of index 2. We use this construction to fully describe the degree one connecting homomorphism on Galois cohomology for all adjoint groups of type E_7 over a real-closed field.

1991 Mathematics Subject Classification: 17A40 (Primary) 11E72, 14L27, 17B25, 20G15 (Secondary)

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