We introduce the notions of self-dual (graded) Hopf algebras and of structurally simple (graded) Hopf algebras. We prove that the self-dual Hopf algebras are structurally simple and provide a construction of self-dual Hopf algebras. Finally, we classify the self-dual quotients of the form T-B(M)/I, where T-B(M) is a path algebra with a graded Hopf algebra structure, and I is a graded admissible Hopf ideal. [References: 14]
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