Search

In this paper, we introduce the concept of transposed BiHom-Poisson (abbr. TBP) algebras which can be constructed by BiHom-Novikov-Poisson algebras. Several useful identities for TBP algebras are provided. We also prove that the tensor products of two (T)BP algebras are closed. The notions of BP 3-Lie algebras and TBP 3-Lie algebras are presented and TBP algebras can induce TBP 3-Lie algebras by two approaches. Finally, we give some examples for the TBP algebras of dimension 2. [ABSTRACT FROM AUTHOR]

In this article, firstly, we introduce the notions of m-smash product monoidal Hom-algebra B # m H and n-smash coproduct monoidal Hom-coalgebra B × n H. Furthermore, the necessary and sufficient conditions for B # m H and B × n H on B ⊗ H to be a monoidal Hom-bialgebra structure are derived, where the conditions are equivalent to that (B , β) is a bialgebra in the (m + n) -Yetter-Drinfeld category. Secondly, we prove that the category is a braided monoidal category. At last, we give two mapping descriptions of Radford (0, 0)-biproduct. Communicated by Jason P. Bell [ABSTRACT FROM AUTHOR]

LetAbe a regular multiplier Hopf algebra., the subcategory ofAℳ𝒴𝒟Aconsisting of finite dimensional objects, is a braidedT-category with the left and right dualities. We also show that to a multiplierT-coalgebra we can also associate another braided T-category. [ABSTRACT FROM AUTHOR]