  By using perverse sheaves on representation spaces of quivers over
$k[t]/(t^n)$ and jet schemes over flag varieties, we construct a geometric
composition algebra $\mathbf K$ under Lusztig's framework on geometric
realizations of the negative part of quantum algebras. Simple perverse sheaves
in $\mathbf K$ form the canonical basis of $\mathbf K$. The relationships among
the algebra $\mathbf K$, the composition algebra of locally projective
representations of quivers over $k[t]/(t^n)$ and quantum generalized Kac-Moody
algebra are provided.
