In this paper, we construct all the indecomposable modules of a class of non-pointed Hopf algebras, which are quotient Hopf algebras of a class of prime Hopf algebras of GK-dimension one. Then the decomposition formulas of the tensor product of any two indecomposable modules are established. Based on these results, the representation ring of the Hopf algebras is characterized by generators and some relations.
Citation: Ruifang Yang, Shilin Yang. Representations of a non-pointed Hopf algebra[J]. AIMS Mathematics, 2021, 6(10): 10523-10539. doi: 10.3934/math.2021611
In this paper, we construct all the indecomposable modules of a class of non-pointed Hopf algebras, which are quotient Hopf algebras of a class of prime Hopf algebras of GK-dimension one. Then the decomposition formulas of the tensor product of any two indecomposable modules are established. Based on these results, the representation ring of the Hopf algebras is characterized by generators and some relations.
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Ruifang Yang, Shilin Yang. Representations of a non-pointed Hopf algebra[J]. AIMS Mathematics, 2021, 6(10): 10523-10539. doi: 10.3934/math.2021611
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