  Let $G$ be a connected reductive algebraic group $G$ over an algebraically
closed field $k$ of prime characteristic $p$, and $\ggg=\Lie(G)$. In this
paper, we study modular representations of the reductive Lie algebra $\ggg$
with $p$-character $\chi$ of standard Levi-form associated with an index subset
$I$ of simple roots. With aid of support variety theory we prove a theorem that
a $U_\chi(\ggg)$-module is projective if and only if it is a strong "tilting"
module, i.e. admitting both $\cz_Q$- and $\cz^{w^I}_Q$-filtrations (to see
Theorem \ref{THMFORINV}). Then by analogy of the arguments in \cite{AK} for
$G_1T$-modules, we construct so-called Andersen-Kaneda filtrations associated
with each projective $\ggg$-module of $p$-character $\chi$, and finally obtain
sum formulas from those filtrations.
