What is contragredient about contragrediant Lie superalgebras

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Among the Lie superalgebras there is the class of contragredient Lie superalgebras. Roughly speaking these are those Lie superalgebras that can be defined with a matrix $a_{ij}$ and commutation relations of the generators $H_i,E_i$ and $F_i$ which are

$$ [H_i,E_j]=a_{ij}E_j,\quad [H_i,F_j]=a_{ij}F_j, \quad [E_i,F_j]=\delta_{ij}H_i. $$

For the detailed definition see e.g. Serganova (Sec. 2, denoted by $\mathfrak{g}(A)$).

My questions is: what is the meaning of "contragredient" in this context? That is what is the definition of the property "contragredient" and how is it fulfilled by these algebras?