In this paper, all simple Yetter-Drinfeld modules and indecomposable projective Yetter-Drinfeld modules over a family of non-pointed $ 8m $-dimension Hopf algebras of tame type with rank two, are construted and classified. The technique is Radford's method of constructing Yetter-Drinfeld modules over a Hopf algebra. Furthermore, the projective class rings of the category of Yetter-Drinfeld modules over this class of Hopf algebras are described explicitly by generators and relations.
Citation: Yaguo Guo, Shilin Yang. Projective class rings of a kind of category of Yetter-Drinfeld modules[J]. AIMS Mathematics, 2023, 8(5): 10997-11014. doi: 10.3934/math.2023557
In this paper, all simple Yetter-Drinfeld modules and indecomposable projective Yetter-Drinfeld modules over a family of non-pointed $ 8m $-dimension Hopf algebras of tame type with rank two, are construted and classified. The technique is Radford's method of constructing Yetter-Drinfeld modules over a Hopf algebra. Furthermore, the projective class rings of the category of Yetter-Drinfeld modules over this class of Hopf algebras are described explicitly by generators and relations.
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Yaguo Guo, Shilin Yang. Projective class rings of a kind of category of Yetter-Drinfeld modules[J]. AIMS Mathematics, 2023, 8(5): 10997-11014. doi: 10.3934/math.2023557
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