Nichols algebras over weak Hopf algebras
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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  are generalized.
Keywordsquantum enveloping algebra Nichols algebra weak Hopf algebra
MR Subject Classification17B37 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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