Special Lie superalgebras with maximality condition for subalgebras (Q658943)

Finitely generated Lie superalgebras over a field of characteristic zero satisfying Capelli identities are considered in the present paper. It is proved that such an algebra with the maximality condition for abelian subalgebras is finite dimensional. In particular, any special Lie superalgebra with the maximality condition for its subalgebras has a finite dimension. It is also proved that the universal enveloping algebra \(U(L)\) of special Lie superalgebra \(L\) is Noetherian if and only if \(\dim\, L <\infty\).