Gilmartin, P. (2019) A note on the order of the antipode of a pointed Hopf algebra. Communications in Algebra, 47(7), pp. 2833-2842. (doi: 10.1080/00927872.2018.1541459)
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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.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | GILMARTIN, Paul |
Authors: | Gilmartin, P. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Communications in Algebra |
Publisher: | Taylor & Francis |
ISSN: | 0092-7872 |
ISSN (Online): | 1532-4125 |
Published Online: | 24 January 2019 |
Copyright Holders: | Copyright © 2019 Taylor and Francis |
First Published: | First published in Communications in Algebra 47(7):2833-2842 |
Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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