In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain ...In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.展开更多
Let (C,α) and (H, β) be Hom-bialgebras and ω : C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct (Cω H, γ) and give necessary and sufficient conditions for (Cω H, γ) to be...Let (C,α) and (H, β) be Hom-bialgebras and ω : C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct (Cω H, γ) and give necessary and sufficient conditions for (Cω H, γ) to be a Hom-bialgebra. We study the quasi-triangular structures over (Cω H, γ) and show the necessary and sufficient conditions for (Cω H, γ R) to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D(H)* and construct quasi-triangular structures over D(H)*.展开更多
基金Supported by the National Natural Science Foundation of China(11047030, 11171055) Supported by the Grant from China Scholarship Counci1(2011841026)
文摘In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.
基金Supported by the National Natural Science Foundation of China(60873267)the Ningbo Natural Science Foundation of China(2011A610172)K.C.Wang Magna Fund in Ningbo University
文摘Let (C,α) and (H, β) be Hom-bialgebras and ω : C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct (Cω H, γ) and give necessary and sufficient conditions for (Cω H, γ) to be a Hom-bialgebra. We study the quasi-triangular structures over (Cω H, γ) and show the necessary and sufficient conditions for (Cω H, γ R) to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D(H)* and construct quasi-triangular structures over D(H)*.