Derivation-simple algebras and the structures of Lie algebras of Witt type
The authors classify all pairs \((\{ \mathfrak A\}, {\mathfrak D})\) where \(\mathfrak A\) is a commutative associative algebra with identity over an algebraically closed field of characteristic 0, and \(\mathfrak D\) is its finite-dimensional locally finite Abelian derivation subalgebra, such that \(\mathfrak A\) is derivation-simple with respect to \(\mathfrak D\). They also determine the isomorphism classes of the simple Lie algebras of Witt type, which are constructed from such pairs, and explicitly give the structure spaces of these algebras.
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