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تسجيل مستخدم جديدInvolutions of sl(2,k) and non-split, three-dimensional simple Lie algebras
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تأليف
Philippe Meyer
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We give a process to construct non-split, three-dimensional simple Lie algebras from involutions of sl(2,k), where k is a field of characteristic not two. Up to equivalence, non-split three-dimensional simple Lie algebras obtained in this way are parametrised by a subgroup of the Brauer group of k and are characterised by the fact that their Killing form represents -2. Over local and global fields we re-express this condition in terms of Hilbert and Legendre Symbols and give examples of three-dimensional simple Lie algebras which can and cannot be obtained by this construction over the field of rationals.
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