we explore the (noncommutative) geometry of representations of locally finite lie algebras. let l be one of these lie algebras, and let i in u(l) be the annihilator of a locally simple l-module. we show that for each such i, there is a quiver q so that locally simple l-modules with annihilator i are parameterized by "points" in the "noncommutative space" corresponding to the path algebra of q. we classify the quivers that occur and along the way discover a beautiful connection to characters of the symmetric groups $s_n$.