Hopf -crossed biproduct and related coquasitriangular structures
A construction of the Hom-Yetter-Drinfeld category
In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter-Drinfeld category via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter-Drinfeld modules can provide solutions of the Hom-Yang-Baxter equation and is a pre-braided tensor category, where (H,β,S) is a Hom-Hopf algebra. Furthermore, we show that is a Radford biproduct Hom-Hopf algebra if and only if (A,α) is a Hom-Hopf algebra in the category . Finally,...
Cobraided smash product Hom-Hopf algebras
Let (A,α) and (B,β) be two Hom-Hopf algebras. We construct a new class of Hom-Hopf algebras: R-smash products . Moreover, necessary and sufficient conditions for to be a cobraided Hom-Hopf algebra are given.
A new approach to antisymmetric infinitesimal bialgebras
We present a notion of an anti-covariant bialgebra extending the anti-symmetric infinitesimal bialgebra and also provide some equivalent characterizations of it. We also prove that an anti-associative Yang-Baxter pair can produce a special Rota-Baxter system.
Products of integral-type and composition operators between generally weighted Bloch spaces.
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