BiHom-H-pseudoalgebras and their constructions

BiHom-H-伪代数及其构造（英文）

The definition and an example of BiHom-associative H-pseudoalgebra are given.A BiHom-H-pseudoalgebra is an H-pseudoalgebra(A,μ)with two mapsα,β∈HomH(A,A)satisfying the BiHom-associative law which generalizes BiHom-associative algebras and associative H-pseudoalgebras.Secondly,a method which is called the Yau twist of constructing BiHom-associative H-pseudoaglebra(A,(IH■H■Hα)μ,α,β)from an associative H-pseudoalgebra(A,μ)and two maps of H-pseudoalgebrasα,β,is introduced.Thirdly,a generalized form of the Yau twist is discussed.It concerns constructing a BiHom-associative H-pseudoalgebra(A,μ(α■β),α^~α,β^~β)from a BiHom-associative H-pseudoalgebra(A,μ,α^~,β^~)and two mapsα,β∈Hom H(A,A).Finally,a method of constructing BiHom-associative H-pseudoalgebra on tensor product space A■B of two BiHom-associative H-pseudoalgebras is given.

首先,给出了BiHom-结合H-伪代数的定义与例子,一个BiHom-结合H-伪代数由一个H-伪代数(A,μ)和满足BiHom-结合律的2个映射α,β∈HomH(A,A)构成,其为BiHom-结合代数和结合H-伪代数的推广.然且,介绍了名为Yau扭曲的方法,该方法是由一个结合H-伪代数(A,μ)和2个H-伪代数同态α,β构造BiHom-结合H-伪代数(A,(IH■H■Hα)μ,α,β).同时,介绍了Yau扭曲的推广形式,即由一个BiHom-结合H-伪代数(A,μ,α^~,β^~)和2个映射α,β∈HomH(A,A)构造BiHom-结合H-伪代数(A,μ(α■β),α^~α,β^~β).最后,给出了在2个BiHom-结合H-伪代数的张量积空间A■B上构造BiHom-结合H-伪代数的方法.