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An Application of Rafael＇s Theorem over Partial Entwined Modules

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Algebra Colloquium 2016年第1期23卷 89-96页

作者： ShengxiangWang shuangjian guo Department of Mathematics Nanjing University Nanjing 210093 China School of Mathematics and Finance Chuzhou University Chuzhou Anhui 239000 China School of Mathematics and Statistics Guizhou University of Finance and Economics Guizhou 550025 China

We obtain necessary and sufficient conditions for the functor F ： ∪/Ac （ψ） → Mc on the category of partial entwined modules that forgets the A-action to be separable. As an application, we prove a Maschke-type t... 详细信息

关键词： partial entwined module cointegral Maschke-type theorem

Quasitriangular Turaev Group Coalgebras and Radford＇s Biproduct

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Algebra Colloquium 2016年第3期23卷 427-442页

作者： shuangjian guo ShuanhongWang School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang 550025 China Department of Mathematics Southeast University Nanjing 210096 China

In this paper, we construct a new example of Hopf group coalgebras by con- sidering Radford＇s biproduct Hopf algebra in the Turaev category. Furthermore, we find some sufficient and necessary conditions for such Radf... 详细信息

关键词： Turaev category Radford's biproduct Hopf algebra Turaev group coalgebra,quasitriangular Turaev group coalgebra

Matching Rota-Baxter Systems and Gröbner-Shirshov Bases

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Algebra Colloquium 2024年第3期31卷 389-406页

作者： Yi Zhang shuangjian guo School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044China School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang 550025China

Motivated by the concept of matching Rota-Baxter algebras arising from polarized associative Yang-Baxter equations and Volterra integral equations,we introduce the notion of a matching Rota-Baxter system,which generalizes the Rota-Baxter system proposed by *** show that this notion is also related to Yang-Baxter pairs and to matching pre-Lie *** then modify the definition of matching Rota-Baxter systems by adding a curvature term,and make a connection with matching pre-Lie algebras and with compatible associative ***,we study matching Rota-Baxter systems on a dendriform algebra and show how they induce matching quadri-algebra ***,we give a linear basis of free matching Rota-Baxter system by Grobner-Shirshov bases methods.

关键词： Rota-Baxter systems curved matching Rota-Baxter systems Gröbner-Shirshov bases

Rota-Baxter Family Systems and Gr?bner-Shirshov Bases

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Journal of Mathematical Research with Applications 2023年第2期43卷 175-190页

作者： shuangjian guo School of Mathematics and Statistics Guizhou University of Finance and Economics

Motivated by the concept of Rota-Baxter family algebras arising from associative Yang-Baxter family equations and Volterra integral equations, we introduce the notion of a Rota-Baxter family system which generalizes the Rota-Baxter system proposed by Brzeziń*** show that this notion is also related to an associative Yang-Baxter family pair and the preLie family algebras. Furthermore, as an analogue of Rota-Baxter family system, we introduce a notion of averaging family system and prove that an averaging family system induces a dialgebra family structure. We also study Rota-Baxter family systems on a dendriform algebra and show how they induce quadri family algebra structures. Finally, we give a linear basis of the RotaBaxter family system by the methods of Gr?bner-Shirshov bases.

关键词： Rota-Baxter family systems Rota-Baxter family algebras Grobner-Shirshov bases

Central Extensions and Deformations of Lie Triple Systems with a Derivation

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Journal of Mathematical Research with Applications 2022年第2期42卷 189-198页

作者： shuangjian guo School of Mathematics and Statistics Guizhou University of Finance and Economics

In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with coefficients in a representation. We study central extensions of a LietsDer pair. In the next, we generalize the formal deformation theory to LietsDer pairs in which we deform both the Lie triple system bracket and the distinguished derivation. It is governed by the cohomology of LietsDer pair with coefficients in itself.

关键词： Lie triple system derivation representation cohomology central extension deformation

Cohomology of Lie-Conformal Algebras with Derivations

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Journal of Mathematical Research with Applications 2024年第6期44卷 754-768页

作者： shuangjian guo School of Mathematics and Statistics Guizhou University of Finance and Economics

In this paper, we consider Lie conformal algebras with derivations. A pair consisting of a Lie conformal algebra and a distinguished derivation is called a LieCDer pair. We introduce a cohomology theory for LieCDer pair with coefficients in a representation. Furthermore, we study abelian extensions of a LieCDer pair as an application of cohomology theory. Finally, we consider homotopy derivations on 2-term conformal L∞-algebras and 2-derivations on conformal Lie 2-algebras. The category of 2-term conformal L∞-algebras with homotopy derivations is equivalent to the category of conformal Lie 2-algebras with 2-derivations.

关键词： Lie conformal algebras cohomology abelian extension conformal Lie 2-algebras homotopy derivation

On Split Regular Hom-Poisson Color Algebras

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Journal of Mathematical Research with Applications 2019年第5期39卷 495-505页

作者： shuangjian guo School of Mathematics and Statistics Guizhou University of Finance and Economics

We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show∑that such a split regular Hom-Poisson color algebras A is of the form A = U +αIα with U a subspace of a maximal abelian subalgebra H and any Iα, a well described ideal of A, satisfying[Iα, Iβ] + IαIβ = 0 if [α]≠[β]. Under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized.

关键词： Hom-Lie color algebra Hom-Poisson color algebra root structure theory

Coquasitriangular Weak Hopf Group Algebras and Braided Monoidal Categories

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Journal of Mathematical Research with Applications 2014年第6期34卷 655-668页

作者： shuangjian guo School of Mathematics and Statistics Guizhou University of Finance and Economics

In this paper, we first give the definitions of a crossed left π-H-comodules over a crossed weak Hopf π-algebra H, and show that the category of crossed left π-H-comodules is a monoidal category. Finally, we show that a family σ = {σα,β: Hα Hβ→ k}α,β∈πof k-linear maps is a coquasitriangular structure of a crossed weak Hopf π-algebra H if and only if the category of crossed left π-H-comodules over H is a braided monoidal category with braiding defined by σ.

关键词： π-H-comodules braided monoidal category coquasitriangular structure

Double Constructions of Frobenius Hom-Algebras and Connes Cocycles

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Journal of Mathematical Research with Applications 2020年第6期40卷 577-595页

作者： shuangjian guo Lihong DONG School of Mathematics and Statistics Guizhou University of Finance and Economics College of Mathematics and Information Science Henan Normal University

In this paper, we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras. Furthermore, we study the double constructions of Connes cocycles in terms of Hom-dendriform algebras. Finally, we give a clear analogy between antisymmetric infinitesimal Hom-bialgebras and Hom-dendriform D-bialgebras.

关键词： Frobenius Hom-algebras Hom-dendriform algebras $\mathcal{O}$-operators antisymmetric infinitesimal Hom-bialgebras Hom-dendriform $D$-bialgebras