Central simple algebras with involution: A geometric approach

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Let k be an algebraically closed base field of characteristic zero. The category equivalence between central simple algebras and irreducible, generically free PGL n -varieties is extended to the context of central simple algebras with involution. The associated variety of a central simple algebra with involution comes with an action of PGLn× 〈τ〉, where τ is the automorphism of PGL n given by τ (h) = (h -1)transpose. Basic properties of an involution are described in terms of the action of PGLn× 〈τ〉 on the associated variety, and in particular in terms of the stabilizer in general position for this action.

Original languageEnglish
Pages (from-to)453-467
Number of pages15
JournalManuscripta Mathematica
Issue number4
StatePublished - Apr 2009


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