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Construction of a class of H-pseudoalgebras

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Journal of Southeast University(English Edition) 2017年第4期33卷 517-520页

作者： Liu Linlin wang shuanhong School of Mathematics Southeast University Nanjing 211189 China

Let H be a cocommutative Hopf ***,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(*** multiplication)of Hon itself into an adjoint ***,a class o f{H,R)-pseudoalgebras are studied by generalizing the aboveconstruction when(H,R)is a quasitrianglar Hopf algebra.A tthe same time,the(H,R)-pseudoalgebra is constructed byboth the usual algebra and the tensor product o f(H,R)-***,some examples of the(H,R)-pseudoalgebra are given explicitly,and the conditions for aHopf algebra to be an(H,R)-pseudoalgebra(***)are discussed.

关键词： cocommutative Hopf algebra H-pseudoalgebra H-pseudoalgebra ( H ,R) -pseudoalgebra

Sweedler's dual of Hopf algebras in HHYDQCM

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Journal of Southeast University(English Edition) 2020年第3期36卷 364-366页

作者： Zhang Tao wang shuanhong School of Mathematics Southeast University Nanjing 211189 China

Firstly,the notion of the left-left Yetter-Drinfeld quasicomodule M=(M,·,ρ)over a Hopf coquasigroup H is given,which generalizes the left-left Yetter-Drinfeld module over Hopf ***,the braided monoidal category HHYDQCM is introduced and the specific structure maps are ***,Sweedler's dual of infinite-dimensional Hopf algebras in HHYDQCM is *** proves that if(B,mB,μB,ΔB,εB)is a Hopf algebra in HHYDQCM with antipode SB,then(B^0,(mB0)^op,εB^*,(ΔB0)^op,μB^*)is a Hopf algebra in HHYDQCM with antipode SB^*,which generalizes the corresponding results over Hopf algebras.

关键词： Hopf(co)quasigroup Yetter-Drinfeld quasi(co)module braided monoidal category duality

Diagonal crossed product of multiplier Hopf algebras

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Journal of Southeast University(English Edition) 2020年第2期36卷 241-244页

作者： Yan Dongdong wang shuanhong School of Mathematics Southeast University Nanjing 211189 China

Let A and B be two regular multiplier Hopf ***,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal crossed product in the sense of Hopf *** result that the product in B#A is non-degenerate is ***,the definition of the comultiplicationΔ#on B#A is introduced,which is composed of the multiplierΔB(b)on B⊗B and the multiplierΔA(a)on A⊗A,and the elementΔ#(b⊗a)is a two-side multiplier of B#A⊗B#A,for any b∈B and a∈***,a sufficient condition for B#A to be a regular multiplier Hopf algebra is *** particular,Delvaux's main theorem in the case of smash products is ***,these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.

关键词： multiplier Hopf algebra bimodule algebra diagonal crossed product

BiHom-H-pseudoalgebras and their constructions

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Journal of Southeast University(English Edition) 2019年第2期35卷 269-272页

作者： Shi Guodong wang shuanhong School of Mathematics Southeast UniversityNanjing 211189China

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 ***,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 ***,a generalized form of the Yau twist is *** 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.

关键词： BiHom-associative H-pseudoalgebrsa Yau twist tensor product BiHom-associative H-pseudoalgebras

Galois linear maps and their construction

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Journal of Southeast University(English Edition) 2019年第4期35卷 522-526页

作者： Gu Yue wang Wei wang shuanhong School of Mathematics Southeast UniversityNanjing 211189China Nanjing Research Institute of Electronic Engineering Nanjing 210007China

The condition of an algebra to be a Hopf algebra or a Hopf(co)quasigroup can be determined by the properties of Galois linear *** a bialgebra H,if it is unital and associative as an algebra and counital coassociative as a coalgebra,then the Galois linear maps T1 and T2 can be *** such a bialgebra H,it is a Hopf algebra if and only if T1 is ***,T1^-1 is a right H-module map and a left H-comodule map(similar to T2).On the other hand,for a unital algebra(no need to be associative),and a counital coassociative coalgebra A,if the coproduct and counit are both algebra morphisms,then the sufficient and necessary condition of A to be a Hopf quasigroup is that T1 is bijective,and T1^-1 is left compatible with ΔT1-11^r and right compatible with mT1-1^l at the same time(The properties are similar to T2).Furthermore,as a corollary,the quasigroups case is also considered.

关键词： Galois linear map antipode Hopf algebra Hopf(co)quasigroup

Fundamentals of quasigroup Hopf group-coalgebras

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Journal of Southeast University(English Edition) 2021年第1期37卷 114-118页

作者： Zhang Senlin wang shuanhong School of Mathematics Southeast UniversityNanjing 211189China

A large class of algebras(possibly nonassociative)with group-coalgebraic structures,called quasigroup Hopf group-coalgebras,is introduced and *** Hopf group-coalgebras provide a unifying framework for the classical Hopf algebras and Hopf group-coalgebras as well as Hopf ***,basic results similar to those in Hopf algebras H are proved,such as anti-(co)multiplicativity of the antipode S:H→H,and S^(2)=id if H is commutative or cocommutative.

关键词： Hopf quasigroup group-coalgebra quasigroup Hopf group-coalgebra convolution algebra

Crossed products for Hopf group-algebras

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Journal of Southeast University(English Edition) 2021年第3期37卷 339-342页

作者： You Miman Lu Daowei wang shuanhong School of Mathematics and Information Science North China University of Water Resources and Electric Power Zhengzhou 450045 China Department of Mathematics Jining University Qufu 273155 China School of Mathematics Southeast University Nanjing 211189 China

First,the group crossed product over the Hopf group-algebras is defined,and the necessary and sufficient conditions for the group crossed product to be a group algebra are *** cleft extension theory of the Hopf group algebra is introduced,and it is proved that the crossed product of the Hopf group algebra is equivalent to the cleft *** necessary and sufficient conditions for the crossed product equivalence of two Hopf groups are then ***,combined with the equivalence theory of the Hopf group crossed product and cleft extension,the group crossed product constructed by the general 2-cocycle as algebra is determined to be isomorphic to the group crossed product of the 2-cocycle with a convolutional invertible map of the *** unit property of a general 2-cocycle is equivalent to the convolutional invertible map of the 2-cocycle,and the combination condition of the weak action is equivalent to the convolutional invertible map of the 2-cocycle and the combination condition of the weak ***,crossed product algebra constructed by the general 2-cocycle is isomorphic to the Hopfπ-crossed product algebra constructed by the 2-cocycle with a convolutional invertible map.

关键词： Hopfπ-algebra cleft extension theorem π-comodule-like algebra group crossed products

扭曲Smash积的辫Monoidal范畴与辫Monoidal范畴上的扭曲Smash积

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数学学报（中文版） 1999年第3期42卷 385-394页

作者：王栓宏河南师范大学数学系复旦大学数学所

得出了扭曲Ｓｍａｓｈ积模范畴Ａ＊ＨＭ是辫ｍｏｎｏｉｄａｌ范畴的一个充要条件；进一步讨论了与范畴Ａ—ＨＭ等价的范畴，引进了广义Ｙｅｔｔｅｒ－Ｄｒｉｎｆｅｌｄ范畴ＨＭＣ；最后，给出了辫Ｍｏｎｏｉｄａｌ范畴上扭曲Ｓｍａｓｈ... 详细信息

得出了扭曲Ｓｍａｓｈ积模范畴Ａ＊ＨＭ是辫ｍｏｎｏｉｄａｌ范畴的一个充要条件；进一步讨论了与范畴Ａ—ＨＭ等价的范畴，引进了广义Ｙｅｔｔｅｒ－Ｄｒｉｎｆｅｌｄ范畴ＨＭＣ；最后，给出了辫Ｍｏｎｏｉｄａｌ范畴上扭曲Ｓｍａｓｈ积构成Ｈｏｐｆ代数充要的条件，这些结果统一了量子群中许多重要结论。

关键词：扭曲Smash积辫monoidal范畴 Hopf代数量子群

Construction of new bornological quantum groups based on Galois objects

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Journal of Southeast University(English Edition) 2016年第4期32卷 524-526页

作者：周楠王栓宏东南大学数学系南京211189

Let A be a bornological quantum group and R a bornological algebra. If R is an essential A-module, then there is a unique extension to M（A）-module with 1x = x. There is a one-to-one corresponding relationship between the actions of A and the coactions of . If R is a Galois object for A, then there exists a faithful δ-invariant functional on R. Moreover,the Galois objects also have modular properties such as algebraic quantum groups. By constructing the comultiplication Δ,counit ε, antipode S and invariant functional φ onR×R, R×R can be considered as a bornological quantum group.

关键词： bornological quantum groups actions and coactions Galois theory Galois objects