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december 2016 The Projective Class Rings of a family of pointed Hopf algebras of Rank two
Hui-Xiang Chen, Hassen Suleman Esmael Mohammed, Weijun Lin, Hua Sun
Bull. Belg. Math. Soc. Simon Stevin 23(5): 693-711 (december 2016). DOI: 10.36045/bbms/1483671621

Abstract

In this paper, we compute the projective class rings of the tensor product $\mathcal{H}_n(q)=A_n(q)\ot A_n(q^{-1})$ of Taft algebras $A_n(q)$ and $A_n(q^{-1})$, and its cocycle deformations $H_n(0,q)$ and $H_n(1,q)$, where $n>2$ is a positive integer and $q$ is a primitive $n$-th root of unity. It is shown that the projective class rings $r_p(\mathcal{H}_n(q))$, $r_p(H_n(0,q))$ and $r_p(H_n(1,q))$ are commutative rings generated by three elements, three elements and two elements subject to some relations, respectively. It turns out that even $\mathcal{H}_n(q)$, $H_n(0,q)$ and $H_n(1,q)$ are cocycle twist-equivalent to each other, they are of different representation types: wild, wild and tame, respectively.

Citation

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Hui-Xiang Chen. Hassen Suleman Esmael Mohammed. Weijun Lin. Hua Sun. "The Projective Class Rings of a family of pointed Hopf algebras of Rank two." Bull. Belg. Math. Soc. Simon Stevin 23 (5) 693 - 711, december 2016. https://doi.org/10.36045/bbms/1483671621

Information

Published: december 2016
First available in Project Euclid: 6 January 2017

zbMATH: 06682397
MathSciNet: MR3593570
Digital Object Identifier: 10.36045/bbms/1483671621

Subjects:
Primary: 16G60 , 16T05

Keywords: Green ring , indecomposable module , Taft algebra

Rights: Copyright © 2016 The Belgian Mathematical Society

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Vol.23 • No. 5 • december 2016
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