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Examples of Non-Semisimple Hopf Algebra Actions on Artin-Schelter Regular Algebras

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Abstract

Let \(\Bbbk \) be a base field of characteristic p > 0 and let U be the restricted enveloping algebra of a 2-dimensional nonabelian restricted Lie algebra. We classify all inner-faithful U-actions on noetherian Koszul Artin-Schelter regular algebras of global dimension up to three.

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Acknowledgements

The authors thank Ellen Kirkman for useful conversations on the subject and for carefully reading an earlier version of this paper, and thank Yongjun Xu for sharing his unpublished notes [45] and several interesting ideas. H.-X. Chen and D.-G. Wang thank J.J. Zhang and the Department of Mathematics at University of Washington for its hospitality during their visits. H.-X. Chen was partially supported by the National Natural Science Foundation of China (Nos. 12071412 and 11971418). D.-G. Wang was partially supported by the National Natural Science Foundation of China (No. 11871301) and the NSF of Shandong Province (No. ZR2019MA060). J.J. Zhang was partially supported by the US National Science Foundation (Nos. DMS-1700825 and DMS-2001015).

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Authors and Affiliations

  1. School of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, China

    Hui-Xiang Chen

  2. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, China

    Ding-Guo Wang

  3. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195, USA

    James J. Zhang

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  1. Hui-Xiang Chen
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  2. Ding-Guo Wang
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  3. James J. Zhang
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Correspondence to Ding-Guo Wang.

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Chen, HX., Wang, DG. & Zhang, J.J. Examples of Non-Semisimple Hopf Algebra Actions on Artin-Schelter Regular Algebras. Algebr Represent Theor 26, 717–752 (2023). https://doi.org/10.1007/s10468-021-10110-5

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