On hom-Yetter-Drinfeld category

• Let (H, β) be a Hom-Hopf algebra. Recently we introduced the Hom-Yetter-Drinfeld category via Radford biproduct Hom-Hopf algebra, and proved that it is a braided tensor category. Let (H, β, R (or σ)) be a quasitriangular (or cobraided) Hom-Hopf algebra. In this paper, we prove that the category of left (H, β)-Hom-modules (comodules) is a braided tensor subcategory. As a generalization of Radford biproduct Hom-Hopf algebra, we derive necessary and sufficient conditions for R-smash product Hom-algebra and T-smash coproduct Hom-coalgebra to be a Hom-Hopf algebra. At last, two nontrivial examples are given.

Ämnesord

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Nyckelord

Hom-Hopf algebra

Hom-coalgebra

Hom-modules comodule

Smash product

Braided tensor category

Mathematics/Applied Mathematics

matematik/tillämpad matematik

Publikations- och innehållstyp

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