A note on the order of the antipode of a pointed Hopf algebra

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
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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