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2009•Journal of MathematicsRequires access

DUALITY OF BITWISTED HOPF ALGEBRAS

Sun Jian-hua

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Abstract

The aim of this paper is to discuss the gradedly dual space of a bitwisted Hopf algebra,and the gradedly duality relationship between two bitwisted Hopf algebras.By using the properties of the dual space of a graded algebra and coalgebra,we prove that the gradedly dual space of a local finite(χ1,χ2)-bitwisted Hopf algebra is a(χ1T,χ2)-bitwisted Hopf algebra,and then we point out that when we want to prove two bitwisted Hopf algebras to be graded dual as Hopf algebras,we only have to prove that they are graded dual as bitwisted bialgebras.

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What this paper is about

The aim of this paper is to discuss the gradedly dual space of a bitwisted Hopf algebra,and the gradedly duality relationship between two bitwisted Hopf algebras.By using the properties of the dual space of a graded algebra and coalgebra,we prove that the gradedly dual space of a local finite(χ1,χ2)-bitwisted Hopf algebra is a(χ1T,χ2)-bitwisted Hopf algebra,and then we point out that when we want to prove two bitwisted Hopf algebras to be graded dual as Hopf algebras,we only have to prove that they are graded dual as bitwisted bialgebras.

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Available abstract

The aim of this paper is to discuss the gradedly dual space of a bitwisted Hopf algebra,and the gradedly duality relationship between two bitwisted Hopf algebras.By using the properties of the dual space of a graded algebra and coalgebra,we prove that the gradedly dual space of a local finite(χ1,χ2)-bitwisted Hopf algebra is a(χ1T,χ2)-bitwisted Hopf algebra,and then we point out that when we want to prove two bitwisted Hopf algebras to be graded dual as Hopf algebras,we only have to prove that they are graded dual as bitwisted bialgebras.

Key concepts: Hopf algebra, Mathematics, Duality (order theory), Representation theory of Hopf algebras, Dual (grammatical number), Coalgebra, Pure mathematics, Algebra over a field

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