A note on the order of the antipode of a pointed Hopf algebra |
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Authors: | Paul Gilmartin |
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Institution: | Department of Mathematics, School of Mathematics and Statistics, University of Glasgow, Glasgow, Scotland, UK |
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Abstract: | Let k be a field and let H denote a pointed Hopf k-algebra with antipode S. We are interested in determining the order of S. Building on the work done by Taft and Wilson in 7], we define an invariant for H, denoted mH, and prove that the value of this invariant is connected to the order of S. In the case where char k?=?0, it is shown that if S has finite order then it is either the identity or has order 2?mH. If in addition H is assumed to be coradically graded, it is shown that the order of S is finite if and only if mH is finite. We also consider the case where char k?=?p?>?0, generalizing the results of 7] to the infinite-dimensional setting. |
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Keywords: | Hopf algebra noncommutative ring theory Pointed Hopf algebra quantum group |
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