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2009•Journal of Algebra and Its ApplicationsRequires access

THE QUASITRIANGULAR STRUCTURES FOR ω-SMASH COPRODUCT HOPF ALGEBRAS

Zhengming Jiao

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Abstract

In this paper, the quasitriangular structures of ω-smash coproduct Hopf algebras Bω ⋈ H as constructed by Caenepeel, Ion, Militaru and Zhu were studied. Necessary and sufficient conditions for ω-smash coproduct Hopf algebras to be quasitriangular Hopf algebras are given in terms of properties of their components. As applications of our results, some special cases are discussed. Especially, The quasitriangular structures for D(H)* and H4ω ⋈ kℤ2 are constructed.

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What this paper is about

In this paper, the quasitriangular structures of ω-smash coproduct Hopf algebras Bω ⋈ H as constructed by Caenepeel, Ion, Militaru and Zhu were studied. Necessary and sufficient conditions for ω-smash coproduct Hopf algebras to be quasitriangular Hopf algebras are given in terms of properties of their components. As applications of our results, some special cases are discussed. Especially, The quasitriangular structures for D(H)* and H4ω ⋈ kℤ2 are constructed.

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Available abstract

In this paper, the quasitriangular structures of ω-smash coproduct Hopf algebras Bω ⋈ H as constructed by Caenepeel, Ion, Militaru and Zhu were studied. Necessary and sufficient conditions for ω-smash coproduct Hopf algebras to be quasitriangular Hopf algebras are given in terms of properties of their components. As applications of our results, some special cases are discussed. Especially, The quasitriangular structures for D(H)* and H4ω ⋈ kℤ2 are constructed.

Key concepts: Quasitriangular Hopf algebra, Coproduct, Hopf algebra, Mathematics, Pure mathematics, Algebra over a field, Division algebra, Algebra representation

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