Title: On simple reducible depth-two Lie algebras with classical reductive null component
Abstract: We classify the simple finite-dimensional reducible graded Lie algebras of the form ${L_{ - 2}} \oplus {L_{ - 1}} \oplus {L_0} \oplus {L_1} \oplus \cdots \oplus {L_k}$ over an algebraically closed field of characteristic greater than 3, where ${L_0}$ is reductive and classical such that no nonzero element of the center of ${L_0}$ annihilates ${L_{ - 2}}$ and where ${L_{ - 1}}$ is the sum of two proper ${L_0}$-submodules.