Double Biproduct Hom-Bialgebra and Related Quasitriangular Structures

Let （H,β） be a Hom-bialgebra such that β^2 = idH. （A, αA） is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category H^HYD and （B, αB） is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YDH^H. The authors define the two-sided smash product Hom-algebra （A H B, αA β αB） and the t...

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Bibliographic Details
Published in:Chinese annals of mathematics. Serie B 2016-11, Vol.37 (6), p.929-950
Main Authors: Ma, Tianshui, Li, Haiying, Liu, Linlin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Economic models
Mathematics
Mathematics and Statistics
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Summary:Let （H,β） be a Hom-bialgebra such that β^2 = idH. （A, αA） is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category H^HYD and （B, αB） is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YDH^H. The authors define the two-sided smash product Hom-algebra （A H B, αA β αB） and the two-sided smash coproduct Hom- coalgebra （A H B, αA β αB）. Then the necessary and sufficient conditions for （A H B, αA β αB） and （A H B, αA β αB） to be a Hom-bialgebra （called the double biproduct Hom-bialgebra and denoted by （A H B, αA β αB）） are derived. On the other hand, the necessary and sufficient conditions for the smash coproduct Hom-Hopf algebra （A H B, αA β） to be quasitriangular are given.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-016-1001-5