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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 $$L$$.
##### MSC:
 17B50 Modular Lie (super)algebras 17B35 Universal enveloping (super)algebras