Two results on double crossed biproducts

Authors : Tianshui MA, Bei Lİ

Pages : 1121-1140

Doi:10.15672/hujms.997154

View : 21 | Download : 10

Publication Date : 2022-08-01

Article Type : Research Paper

Abstract :Let H H be an algebra with a distinguished element ε H ∈ H ∗ εH∈H∗ and C , D C,D two coalgebras. Based on the construction of Brzeziński’s crossed coproduct, under some suitable conditions, we introduce a coassociative coalgebra C × G T H β R × D C×TGHRβ×D which is a more general two-sided coproduct structure including two-sided smash coproduct. Necessary and sufficient conditions for C × G T H β R × D C×TGHRβ×D equipped with two-sided tensor product algebra C ⊗ H ⊗ D C⊗H⊗D to be a bialgebra insert ignore into journalissuearticles values(Hopf algebra); are provided. On the other hand, we obtain an improved version of the double crossed biproduct C ⋆ α H β ⋆ D C⋆αHβ⋆D in [An extended form of Majid`s double biproduct, J. Algebra Appl. 16  insert ignore into journalissuearticles values(4);, 1760061, 2017] which induces a description of C ⋆ α H β ⋆ D C⋆αHβ⋆D similar to Majid double biproduct C ⋆ H ⋆ D C⋆H⋆D and also present some related structures.
Keywords : crossed coproduct, Radford biproduct, double biproduct