Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type

doi:10.1007/s11464-021-0893-x

Front. Math. China

2021, Vol. 16

Issue (1) : 29-47 https://doi.org/10.1007/s11464-021-0893-x

RESEARCH ARTICLE

Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type

Jialei CHEN¹, Shilin YANG¹(

), Dingguo WANG²

¹. College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China
². School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

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Abstract

We construct the Grothendieck rings of a class of $2 n 2$ dimensional semisimple Hopf Algebras $H 2 n 2$ ,which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra $H 8$ .All irreducible $H 2 n 2$ -modules are classified. Furthermore, we describe the Grothendieck rings $r (H 2 n 2)$ by generators and relations explicitly.

Keywords Grothendieck ring Hopf algebra irreducible module

Corresponding Author(s): Shilin YANG

Issue Date: 26 March 2021

Cite this article:

Jialei CHEN,Shilin YANG,Dingguo WANG. Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type[J]. Front. Math. China, 2021, 16(1): 29-47.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0893-x
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I1/29

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