Automorphisms and Twisted Forms of Generalized Witt Lie Algebras
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چکیده
We prove that the automorphisms of the generalized Witt Lie algebras W(m , n) over arbitrary commutative rings of characteristic p > 3 all come from automorphisms of the algebras on which they are defined as derivations. By descent theory, this result then implies that if a Lie algebra over a field becomes isomorphic to W{m, n) over the algebraic closure, it is a derivation algebra of the type studied long ago by Ree. Furthermore, all isomorphisms of those derivation algebras are induced by isomorphisms of their underlying associative algebras.
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The purpose of this thesis is to give a new construction for central extensions of certain classes of infinite dimensional Lie algebras which include multiloop Lie algebras as motivating examples. The key idea of this construction is to view multiloop Lie algebras as twisted forms. This perspective provides a beautiful bridge between infinite dimensional Lie theory and descent theory and is cru...
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