2008•Journal of Yangzhou UniversityRequires access

The trival extension of coalgebra

Tang Hai-jun

Abstract

This paper introduces the extension of coalgebra(respectively,bialgebra,Hopf algebra),which is similar to the case of algebra.Proves that the trivial extension of a finite dimensional coalgebra is coFrobenius.A sufficient-necessary(respectively,sufficient) condition is given that the extension of bialgebra is a bialgebra(respectively,Hopf algebra).Finally,a class of biFrobenius algebra is presented which is not Hopf algebra.

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Key concepts: Bialgebra, Coalgebra, Hopf algebra, Extension (predicate logic), Mathematics, Algebra over a field, Representation theory of Hopf algebras, Class (philosophy)