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Research Article | Open Access

Module algebra structures of nonstandard quantum group X q ( A 1 ) on the quantum plane

Dong Su1( ), Fengxia Gao2, Zhenzhen Gao1
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
School of Science, Henan Institute of Technology, Xinxiang 453003, China
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Abstract

In this paper, for n ≥ 2 and n ≠ 3, the module algebra structures of X q ( A 1 ) on the quantum n-space were discussed, where the quantum n-space is denoted by A q ( n ). In particular, a complete list of X q ( A 1 )-module algebra structures on the quantum plane A q ( 2 ) was produced and the isomorphism classes of these structures were described.

Keywords

nonstandard quantum groupquantum n-spaceHopf actionmodule algebraweight

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Electronic Research Archive
Volume 33 Issue 6,
June 2025
Pages 3543-3560
DOI: 10.3934/era.2025157

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Cite this article:
Su D, Gao F, Gao Z. Module algebra structures of nonstandard quantum group X q ( A 1 ) on the quantum plane. Electronic Research Archive, 2025, 33(6): 3543-3560. https://doi.org/10.3934/era.2025157

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Received: 03 March 2025
Revised: 20 May 2025
Accepted: 30 May 2025
Published: 09 June 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)