Self-dual weak Hopf algebras |
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Authors: | Munir Ahmed Fang Li |
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Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310027, P. R. China |
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Abstract: | In this paper, we define the notion of self-dual graded weak Hopf algebra and self-dual semilattice graded weak Hopf algebra.
We give characterization of finite-dimensional such algebras when they are in structually simple forms in the sense of E.
L. Green and E. N. Morcos. We also give the definition of self-dual weak Hopf quiver and apply these types of quivers to classify
the finite-dimensional self-dual semilattice graded weak Hopf algebras. Finally, we prove partially the conjecture given by
N. Andruskiewitsch and H.-J. Schneider in the case of finite-dimensional pointed semilattice graded weak Hopf algebra H when grH is self-dual.
Project supported by the Program for New Century Excellent Talents in University (No. 04-0522) and the National Natural Science
Foundation of China (No. 10571153) |
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Keywords: | weak Hopf algebra self-duality weak Hopf quiver |
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