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

A Class of Weak Hopf Algebras

Dongming Cheng1,2

1Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China
2Department of Mathematics, Henan University of Science and Technology, Luoyang, Henan 471003, China

Received 24 November 2009; Accepted 27 January 2010

Academic Editor: Palle Jorgensen

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.

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.