International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 520762, 8 pages
doi:10.1155/2010/520762

A class of weak Hopf algebras.

Abstract

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 Hn has a quotient Hopf algebra and a sub-Hopf algebra which are isomorphic to Hn.