Abstract: Semisimple Lie superalgebras are Lie superalgebras with non-degenerate Killing forms. In this paper we show that a quadratic Lie superalgebra $({\frak g}, B)$ is semisimple if and only if its Casimir operator, $\Omega_B$, associated to $B$ is invertible. This result anables us to characterize quadratic Lie superalgebras with nilpotent Casimir operators: $\Omega_B$ is nilpotent if and only if ${\frak g}$ is a Lie superalgebra without any nonzero semisimple ideal.
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