Hopf Algebras on Schurian Quivers |
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Authors: | Pu Zhang |
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Affiliation: | 1. Department of Mathematics , Shanghai Jiao Tong University , Shanghai, China pzhang@sjtu.edu.cn |
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Abstract: | Let H be a Hopf algebra with a finite-dimensional, nontrivial space of skew primitive elements, over an algebraically closed field of characteristic zero. We prove that H contains either the polynomial algebra as a Hopf subalgebra, or a certain Schurian simple-pointed Hopf subalgebra. As a consequence, a complete list of the locally finite, simple-pointed Hopf algebras is obtained. Also, the graded automorphism group of a Hopf algebra on a Schurian Hopf quiver is determined, and the relation between this group and the automorphism groups of the corresponding Hopf quiver, is clarified. |
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Keywords: | Graded automorphism Schurian Hopf quivers Simple-pointed Hopf algebras |
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