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A construction of the Hom-Yetter-Drinfeld category

100%

Li H., Ma T.

Colloquium Mathematicum

2014

tom 137

nr 1

43-65

In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter-Drinfeld category $_{H}^{H}𝕐𝔻$ via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter-Drinfeld modules can provide solutions of the Hom-Yang-Baxter equation and $_{H}^{H}𝕐𝔻$ is a pre-braided tensor category, where (H,β,S) is a Hom-Hopf algebra. Furthermore, we show that $(A♮_{⋄} H,α⊗ β)$ is a Radford biproduct Hom-Hopf algebra if and only if (A,α) is a Hom-Hopf algebra in the category $_{H}^{H}𝕐𝔻$. Finally, some examples and applications are given.

Cobraided smash product Hom-Hopf algebras

81%

Ma T., Li H., Yang T.

Colloquium Mathematicum

2014

tom 134

nr 1

75-92

Let (A,α) and (B,β) be two Hom-Hopf algebras. We construct a new class of Hom-Hopf algebras: R-smash products $(A ♮_{R} B,α ⊗ β)$. Moreover, necessary and sufficient conditions for $(A ♮_{R} B,α ⊗ β)$ to be a cobraided Hom-Hopf algebra are given.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Li H.

2 Ma T.

1 Yang T.

2 2014

Wyniki wyszukiwania

A construction of the Hom-Yetter-Drinfeld category

Cobraided smash product Hom-Hopf algebras