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 algebraHnhas a quotient Hopf algebra and a sub-Hopf algebra which are isomorphic toHn.
Highlights
Weak Hopf algebra was introduced by Li in 1998 as a generalization of Hopf algebras 1
All examples of weak Hopf algebras were based on some Hopf algebras and were constructed by weak extension
The coalgebra structures of these weak Hopf algebras are described by their Ext quiver 8, 9
Summary
Weak Hopf algebra was introduced by Li in 1998 as a generalization of Hopf algebras 1. All examples of weak Hopf algebras were based on some Hopf algebras and were constructed by weak extension. We first give a Hopf algebra, denoted by Hn. By weak extension, we construct a weak Hopf algebra W n1, n2, n3 corresponding to Hn and study their structure. W n1, n2, n3 has a quotient Hopf algebra and a sub-Hopf algebra which are isomorphic to Hn. And as an algebra, W n1, n2, n3 can be decomposed into a direct sum of two algebras, one of which is Hn. The coalgebra structures of these weak Hopf algebras are described by their Ext quiver 8, 9. We give the Ext-quiver of coalgebra of W n1, n2, n3 and prove that W n1, n2, n3 has a quotient Hopf algebra and a sub-Hopf algebra which are isomorphic to Hn
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