Quasi-quantum planes and quasi-quantum groups of dimension 𝑝³ and 𝑝⁴

Huang, Hua-Lin; Yang, Yuping

doi:10.1090/S0002-9939-2015-12602-0

Quasi-quantum planes and quasi-quantum groups of dimension $p^3$ and $p^4$
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by Hua-Lin Huang and Yuping Yang

Proc. Amer. Math. Soc. 143 (2015), 4245-4260

DOI: https://doi.org/10.1090/S0002-9939-2015-12602-0

Published electronically: March 25, 2015

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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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