We replace the group of group-like elements of the quantized enveloping
algebra Uq(g) of a finite dimensional semisimple Lie algebra
g by some regular monoid and get the weak Hopf algebra
wqd(g). It is a new subclass of weak Hopf algebras
but not Hopf algebras. Then we devote to constructing a basis of
wqd(g) and determine the group of weak Hopf algebra
automorphisms of wqd(g) when q is not a root of
unity.Comment: 21 page