Oriented quantum algebras （coalgebras） are generalizations of quasitriangular Hopf algebras （coquasitriangular Hopf algebras） and account for regular isotopy invariants of oriented 1-1 tangles, oriented knots and ...Oriented quantum algebras （coalgebras） are generalizations of quasitriangular Hopf algebras （coquasitriangular Hopf algebras） and account for regular isotopy invariants of oriented 1-1 tangles, oriented knots and links. Let （H, or, D, U） be an oriented quantum coalgebra over the field k. Then （H×H, φ, D×D, U× U） is a trivial oriented quantum coalgebra structure on the tensor product of coalgebra H with itself, where φ （a × b, c × d） = σ-（ a, c）σ （b, d）. This paper presents the oriented quantum coalgebra structure （ H×H, σ, D×D, U× U） on coalgebra H× H, where σ（ a × b, c× d） = σ ^-1 （ d1, a1 ） σ（ a2, c1 ） σ^-1 （ d2, b1 ） σ（ b2, c2 ）. So a nontrivial oriented quantum coalgebra structure is obtained and it is dual to Radford＇s results in the paper ＂On the tensor product of an oriented quantum algebra with itself＂ published in 2007. Theoretically, the results of this paper are important in constructing the invariants of oriented knots and links.展开更多
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...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.展开更多
基金The National Natural Science Foundation of China(No.10871042)
文摘Oriented quantum algebras （coalgebras） are generalizations of quasitriangular Hopf algebras （coquasitriangular Hopf algebras） and account for regular isotopy invariants of oriented 1-1 tangles, oriented knots and links. Let （H, or, D, U） be an oriented quantum coalgebra over the field k. Then （H×H, φ, D×D, U× U） is a trivial oriented quantum coalgebra structure on the tensor product of coalgebra H with itself, where φ （a × b, c × d） = σ-（ a, c）σ （b, d）. This paper presents the oriented quantum coalgebra structure （ H×H, σ, D×D, U× U） on coalgebra H× H, where σ（ a × b, c× d） = σ ^-1 （ d1, a1 ） σ（ a2, c1 ） σ^-1 （ d2, b1 ） σ（ b2, c2 ）. So a nontrivial oriented quantum coalgebra structure is obtained and it is dual to Radford＇s results in the paper ＂On the tensor product of an oriented quantum algebra with itself＂ published in 2007. Theoretically, the results of this paper are important in constructing the invariants of oriented knots and links.
基金The National Natural Science Foundation of China(No.11371088,11571173,11871144)the Natural Science Foundation of Jiangsu Province(No.BK20171348)
文摘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.
