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| Double Biproduct Hom-Bialgebra and Related Quasitriangular Structures |
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Citation： |
Tianshui MA,Haiying LI,Linlin LIU.Double Biproduct Hom-Bialgebra and Related Quasitriangular Structures[J].Chinese Annals of Mathematics B,2016,37(6):929~950 |
| Page view： 1485
Net amount： 1320 |
Authors： |
Tianshui MA; Haiying LI;Linlin LIU |
Foundation： |
This work was supported by the Henan Provincial Natural Science
Foundation of China (No.17A110007) and the Foundation for Young Key
Teacher by Henan Province (No.2015GGJS-088). |
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| Abstract： |
Let $(H, \b)$ be a Hom-bialgebra such that $\b^2={\rm id}_H$. $(A, \aa)$ is a Hom-bialgebra in
the left-left Hom-Yetter-Drinfeld category $_H^H{\mathbb{YD}}$ and
$(B, \ab)$ is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld
category ${\mathbb{YD}}_H^H$. The authors define the two-sided smash
product Hom-algebra $(A\natural H\natural B, \aa\o \b\o \ab)$ and
the two-sided smash coproduct Hom-coalgebra $(A\diamond H\diamond B,
\aa\o \b\o \ab)$. Then the necessary and sufficient conditions for
$(A\natural H\natural B, \aa\o \b\o \ab)$ and $(A\diamond H\diamond
B, \aa\o \b\o \ab)$ to be a Hom-bialgebra (called the double
biproduct Hom-bialgebra and denoted by $(A^{\natural}_{\diamond}
H^{\natural}_{\diamond} B,\aa\o \b\o \ab)$) are derived. On the
other hand, the necessary and sufficient conditions for the smash
coproduct Hom-Hopf algebra $(A\diamond H,\aa\o \b)$ to be
quasitriangular are given. |
Keywords： |
Double biproduct, Hom-Yetter-Drinfeld category, Radford's biproduct,
Hom-Yang-Baxter equation |
Classification： |
16W30 |
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