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2011•Journal of Algebra and Its ApplicationsRequires access

QUASITRIANGULARITY OF BRZEZIŃSKI'S CROSSED COPRODUCTS

Tianshui Ma, Haiying Li, Shuanhong Wang

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Abstract

In continuation of our recent work about the quasitriangular structures for the twisted tensor biproduct, we give the necessary and sufficient conditions for Brzeziński crossed coproduct coalgebra, including the twisted tensor coproduct introduced by Caenepeel, Ion, Militaru and Zhu and crossed coproduct as constructed by Lin, equipped with the usual tensor product algebra structure to be a Hopf algebra. Furthermore, the necessary and sufficient conditions for Brzeziński crossed coproduct to be a quasitriangular Hopf algebra are obtained.

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What this paper is about

In continuation of our recent work about the quasitriangular structures for the twisted tensor biproduct, we give the necessary and sufficient conditions for Brzeziński crossed coproduct coalgebra, including the twisted tensor coproduct introduced by Caenepeel, Ion, Militaru and Zhu and crossed coproduct as constructed by Lin, equipped with the usual tensor product algebra structure to be a Hopf algebra. Furthermore, the necessary and sufficient conditions for Brzeziński crossed coproduct to be a quasitriangular Hopf algebra are obtained.

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Available abstract

In continuation of our recent work about the quasitriangular structures for the twisted tensor biproduct, we give the necessary and sufficient conditions for Brzeziński crossed coproduct coalgebra, including the twisted tensor coproduct introduced by Caenepeel, Ion, Militaru and Zhu and crossed coproduct as constructed by Lin, equipped with the usual tensor product algebra structure to be a Hopf algebra. Furthermore, the necessary and sufficient conditions for Brzeziński crossed coproduct to be a quasitriangular Hopf algebra are obtained.

Key concepts: Coproduct, Quasitriangular Hopf algebra, Mathematics, Hopf algebra, Coalgebra, Tensor product, Pure mathematics, Algebra over a field

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