Generalized Casimir elements

A method is given for constructing a central element in the universal enveloping algebra $\mathfrak A(L)$ of a Lie algebra $L$, generalizing the method for constructing a Casimir element and not requiring the existence of a nondegenerate invariant form on $L$. Generalized Casimir elements are constructed for certain Lie algebras of Cartan types over a field of positive characteristic.
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