Identities in the universal enveloping algebra for a Lie superalgebra

The author considers Lie superalgebras $L$ over a field of characteristic zero whose universal enveloping algebra $U(L)$ is a $PI$-algebra. Such algebras may be described as follows: the even component $L_0$ of $L$ is Abelian and the odd component $L_1$ contains an $L_0$-submodule $M$ of finite codimension such that the subspace $[L_0, M]$ is finite-dimensional.
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