Abstract
The structure of weak Hopf algebras corresponding to U q (sl 2) are classified by their algebra structure and coalgebra structure. The algebra structure of weak Hopf algebras corresponding to U q (sl 2) can be written as the direct sum of U q (sl 2) and an algebra of polynomials. The coalgebra structure of weak Hopf algebras corresponding to U q (sl 2) are classified by their Ext quiver. There are four types of such structures.
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