  Given an algebraic Lie algebra $\mathfrak{g}$ over $\mathbb{C}$, we
canonically associate to it a Lie algebra $\mathfrak{g}_{\infty}$ defined over
$\mathbb{C}_{\infty}$-the reduction of $\mathbb{C}$ mod infinitely large prime,
and show that for a class of Lie algebras $\mathfrak{g}_{\infty}$ is an
invariant of the derived category of $\mathfrak{g}$-modules. We give two
applications of this construction. First, we show that the bounded derived
category of $\mathfrak{g}$-modules determines algebra $\mathfrak{g}$ for a
class of Lie algebras. Second, given a semi-simple Lie algebra $\mathfrak{g}$
over $\mathbb{C}$, we construct a canonical homomorphism from the group of
automorphisms of the enveloping algebra $\mathfrak{U}\mathfrak{g}$ to the group
of Lie algebra automorphisms of $\mathfrak{g}$, such that its kernel does not
contain a nontrivial semi-simple automorphism. As a corollary we obtain that
any finite subgroup of automorphisms of $\mathfrak{U}\mathfrak{g}$ isomorphic
to a subgroup of Lie algebra automorphisms of $\mathfrak{g}.$
