Copyright © 2010 Dongming Cheng. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We introduce a class of noncommutative and noncocommutative
weak Hopf algebras with infinite Ext quivers and study their structure. We decompose
them into a direct sum of two algebras. The coalgebra structures of these
weak Hopf algebras are described by their Ext quiver. The weak Hopf extension
of Hopf algebra
has a quotient Hopf algebra and a sub-Hopf algebra which are
isomorphic to .