Center construction and duality of category of Hom-Yetter-Drinfeld modules over monoidal Hom-Hopf algebras

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• 作者：Bingliang Shen ; Ling Liu
• 关键词：Monoidal Hom ; Hopf algebra ; Hom ; Yetter ; Drinfeld module ; center construction ; duality
• 刊名：Frontiers of Mathematics in China
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：12
• 期：1
• 页码：177-197
• 全文大小：219 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576
• 卷排序：12

文摘

Let (H,α) be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules _HHH Y D is isomorphic to the center of the category of left (H,α)-Hom-modules. Also, by the center construction, we get that the categories of left-left, left-right, right-left, and right-right Hom-Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Second, we prove that the category of finitely generated projective left-left Hom-Yetter-Drinfeld modules has left and right duality.