  The well-known Loday-Quillen-Tsygan theorem calculates the Lie algebra
homology of the infinite general linear Lie algebra $\mathfrak{gl}(A)$ over an
unital associative algebra $A$. We generalize the Loday-Quillen-Tsygan theorem
to an infinite Lie algebra associated with a (framed) quiver, where we assign
to each vertex $v$ an infinite general linear Lie algebra $\mathfrak{gl}(A_v)$,
to each edge $e$ an infinite matrix module and to each framed vertex a
(anti)-fundamental representation. Given this data, each loop or path ending on
framed vertices of the quiver defined a stratified factorization algebra over
$S^1$ or $[0,1]$ respectively. We show that the corresponding Lie algebra
homology can be expressed as summing the factorization homology over all loops
and framed paths of the quiver.
