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Quasi-quantum planes and quasi-quantum groups of dimension $ p^3$ and $ p^4$


Authors: Hua-Lin Huang and Yuping Yang
Journal: Proc. Amer. Math. Soc. 143 (2015), 4245-4260
MSC (2010): Primary 16T05, 16T20, 16G20
DOI: https://doi.org/10.1090/S0002-9939-2015-12602-0
Published electronically: March 25, 2015
MathSciNet review: 3373924
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Abstract: The aim of this paper is to contribute more examples and classification results of finite pointed quasi-quantum groups within the quiver framework initiated by the first author. The focus is put on finite dimensional graded Majid algebras generated by group-like elements and two skew-primitive elements which are mutually skew-commutative. Such quasi-quantum groups are associated to quasi-quantum planes in the sense of nonassociative geometry. As an application, we obtain an explicit classification of graded pointed Majid algebras with abelian coradical of dimension $ p^3$ and $ p^4$ for any prime number $ p.$


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Additional Information

Hua-Lin Huang
Affiliation: School of Mathematics, Shandong University, Jinan 250100, People’s Republic of China
Email: hualin@sdu.edu.cn

Yuping Yang
Affiliation: School of Mathematics, Shandong University, Jinan 250100, People’s Republic of China
Email: yupingyang@mail.sdu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2015-12602-0
Keywords: Quasi-quantum plane, quasi-quantum group, Hopf quiver
Received by editor(s): November 19, 2013
Received by editor(s) in revised form: May 14, 2014, and June 17, 2014
Published electronically: March 25, 2015
Additional Notes: This work was supported by PCSIRT IRT1264, SRFDP 20130131110001 and SDNSF ZR2013AM022.
The second author is the corresponding author
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2015 American Mathematical Society