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


We construct the Grothendieck rings of a class of 2n2 dimensional semisimple Hopf Algebras \(H_{2n^{2}}\), which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H8. All irreducible \(H_{2n^{2}}\)-modules are classified. Furthermore, we describe the Grothendieck rings r(\(H_{2n^{2}}\)) by generators and relations explicitly.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11671024, 11701019, 11871301) and the Science and Technology Project of Beijing Municipal Education Commission (Grant No. KM202110005012).

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Correspondence to Shilin Yang.

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Chen, J., Yang, S. & Wang, D. Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type. Front. Math. China 16, 29–47 (2021).

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  • Grothendieck ring
  • Hopf algebra
  • irreducible module


  • 16G10
  • 16D70
  • 16T05