Nichols algebras over weak Hopf algebras



In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra ℍ. Although the category of all left ℍ-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra ℍ, and a series of weak Hopf algebras. Some results of [8] are generalized.


quantum enveloping algebra Nichols algebra weak Hopf algebra 

MR Subject Classification

17B37 81R50 


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This article was written in 2013 while I was visiting Department of Mathematics, Hamburg University. I thank Peter Schwergert for valuable discussions and reference. The author would like to thank the referee for careful reading and useful comments on this paper.


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© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical ScienceZhejiang UniversityHangzhouChina

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