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Central elements and invariants in the modular Lie algebras. (English. Russian original) Zbl 1027.17015
Russ. Math. 46, No. 7, 20-24 (2002); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2002, No. 7, 22-26 (2002).
The author seeks analogues in characteristic \(p\) of the result in characteristic zero that the ring \(S^L\) of invariants of the symmetric algebra \(S(L)\) of a Lie algebra \(L\) is isomorphic as an \(L\)-module to the center \(Z(U)\) of the universal enveloping algebra \(U(L)\). The results obtained are for algebras over \(F_p\), the field of \(p\) elements, and involve a certain extension of \(L\).
17B50 Modular Lie (super)algebras
17B35 Universal enveloping (super)algebras