Self-Dual Hopf Quivers |
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| Authors: | Hua-lin Huang Libin Li Yu Ye |
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| Affiliation: | 1. Department of Mathematics , University of Science and Technology of China , Hefei, Anhui, China;2. Mathematics Section , The Abdus Salam International Centre for Theoretical Physics , Trieste, Italy hhuang@ictp.trieste.it;4. Department of Mathematics , Yangzhou University , Yangzhou, Jiangsu, China;5. Department of Mathematics , University of Science and Technology of China , Hefei, Anhui, China |
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| Abstract: | ABSTRACT We study self-dual coradically graded pointed Hopf algebras with a help of the dual Gabriel theorem for pointed Hopf algebras (van Oystaeyen and Zhang, 2004 van Oystaeyen , F. , Zhang , P. ( 2004 ). Quiver Hopf algebras . J. Algebra 280 ( 2 ): 577 – 589 . [CSA] [CROSSREF] [Google Scholar]). The co-Gabriel Quivers of such Hopf algebras are said to be self-dual. An explicit classification of self-dual Hopf quivers is obtained. We also prove that finite dimensional pointed Hopf algebras with self-dual graded versions are generated by group-like and skew-primitive elements as associative algebras. This partially justifies a conjecture of Andruskiewitsch and Schneider (2000 Andruskiewitsch , N. , Schneider , H.-J . ( 2000 ). Finite quantum groups and Cartan matrices . Adv. Math. 154 : 1 – 45 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) and may help to classify finite dimensional self-dual coradically graded pointed Hopf algebras. |
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| Keywords: | Hopf algebra Quiver |
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