Twisted BiHom-smash products and L-R BiHom-smash products for monoidal BiHom-Hopf algebras
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 171-193
MSC: Primary 16T05; Secondary 16T15.
DOI: 10.4064/cm7695-12-2018
Published online: 18 October 2019
Abstract
We construct two new BiHom-algebras from an $H$-BiHom-bimodule algebra $(A,\alpha _{A},\beta _{A})$ and a BiHom-Hopf algebra $(H,\alpha _{H},\beta _{H})$: the twisted BiHom-smash product $A\mathbin{\#^{T}} H$ and the L-R BiHom-smash product $A\mathbin{\natural} H$. We find necessary and sufficient conditions for them to be BiHom-Hopf algebras. Moreover, if $H$ is a BiHom-cocommutative BiHom-Hopf algebra, we prove that $A\mathbin{\#^{T}} H$ and $A\mathbin{\natural} H$ are isomorphic as BiHom-Hopf algebras.
