  In this article, we deal with properties of the reduced Drinfeld double of
the composition subalgebra of the Hall algebra of the category of coherent
sheaves on a weighted projective line. This study is motivated by applications
in the theory of quantized enveloping algebras of some Lie algebras. We obtain
a new realization of quantized enveloping algebras of affine Lie algebras of
simply-laced type and get new embeddings between such algebras. Moreover, our
approach allows to derive new results on the structure of the quantized
enveloping algebras of the toroidal algebras of types $D_4^{(1,1)}$,
$E_6^{(1,1)}$, $E_7^{(1,1)}$ and $E_8^{(1,1)}$. In particular, our method leads
to a construction of a modular action and allows to define a PBW-type basis for
that classes of algebras.
