Nichols algebras over weak Hopf algebras
- 25 Downloads
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
Unable to display preview. Download preview PDF.
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.
- N Andruskiewitsch, H-J Schneider. Pointed Hopf algebras, In: New Directions in Hopf algebras, MSRI Publications, Vol 43, Cambridge University Press, 2002.Google Scholar
- A Joseph. Quantum Groups and Their Primitive Ideals, Ergeb Math Grenzgeb (3), Vol 29, Springer-Verlag, Berlin, 1995.Google Scholar
- S Montgomery. Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, Vol 82, 1993.Google Scholar