  We replace the group of group-like elements of the quantized enveloping
algebra $U_q({\frak{g}})$ of a finite dimensional semisimple Lie algebra
${\frak g}$ by some regular monoid and get the weak Hopf algebra
${\frak{w}}_q^{\sf d}({\frak g})$. It is a new subclass of weak Hopf algebras
but not Hopf algebras. Then we devote to constructing a basis of
${\frak{w}}_q^{\sf d}({\frak g})$ and determine the group of weak Hopf algebra
automorphisms of ${\frak{w}}_q^{\sf d}({\frak g})$ when $q$ is not a root of
unity.
