The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvab...The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.展开更多
The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case ...The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case of the Hom-Lie superalgebras. We present some construction theorems of Hom-Lie H-pseudo-superalgebras, reformulate the equivalent definition of Hom-Lie H-pseudo-super-algebras, and consider the cohomology theory of Hom-Lie H-pseudo-superalgebras with coefficients in arbitrary Hom-modules as a generalization of Kac’s result.展开更多
Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,a class o f{...Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,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)-pseudoalgebras.Finally,some examples of the(H,R)-pseudoalgebra are given explicitly,and the conditions for aHopf algebra to be an(H,R)-pseudoalgebra(resp.Hpseudoalgebra)are discussed.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
In this article,we construct free centroid hom-associative algebras and free centroid hom-Lie algebras.We also construct some other relatively free centroid hom-associative algebras by applying the Gr?bner-Shirshov ba...In this article,we construct free centroid hom-associative algebras and free centroid hom-Lie algebras.We also construct some other relatively free centroid hom-associative algebras by applying the Gr?bner-Shirshov basis theory for(unital)centroid hom-associative algebras.Finally,we prove that the"Poincaré-Birkhoff-Witt theorem"holds for certain type of centroid hom-Lie algebras over a field of characteristic 0,namely,every centroid hom-Lie algebra such that the eigenvectors of the mapβlinearly generates the whole algebra can be embedded into its universal enveloping centroid hom-associative algebra,and the linear basis of the universal enveloping algebra does not depend on the multiplication table of the centroid hom-Lie algebra under consideration.展开更多
On Hom-Lie algebras and superalgebras,we introduce the notions of biderivations and linear commuting maps,and compute them for some typical Hom-Lie algebras and superalgebras,including the q-deformed W(2,2)algebra,the...On Hom-Lie algebras and superalgebras,we introduce the notions of biderivations and linear commuting maps,and compute them for some typical Hom-Lie algebras and superalgebras,including the q-deformed W(2,2)algebra,the q-deformed Witt algebra and superalgebra.展开更多
This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W（2, 2） algebra. We show that the q-deformed W（2, 2） algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspon...This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W（2, 2） algebra. We show that the q-deformed W（2, 2） algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed W（2, 2） algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras.As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W（2, 2） algebra.展开更多
The aim of this paper is to introduce and study Hom-Gel＇fand-Dorfman super-bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing Hom- Gel＇fand-Dorfman super-bialge...The aim of this paper is to introduce and study Hom-Gel＇fand-Dorfman super-bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing Hom- Gel＇fand-Dorfman super-bialgebras. Also, we obtain some infinite-dimensional Hom-Lie superalgebras from affinization of Hom-Gel＇fand-Dorfman super-bialgebras. Finally, we give a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras and establish the equivalence between quadratic Hom-Lie conformal superalgebras and Hom-Gel＇fand-Dorfman super-bialgebras.展开更多
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie con...The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce α~k-derivations of multiplicative Hom-Lie conformal algebras and study their properties.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（11071187） Supported by the Natural Science Foundation of Henan Province（13A110785）
文摘The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.
文摘The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case of the Hom-Lie superalgebras. We present some construction theorems of Hom-Lie H-pseudo-superalgebras, reformulate the equivalent definition of Hom-Lie H-pseudo-super-algebras, and consider the cohomology theory of Hom-Lie H-pseudo-superalgebras with coefficients in arbitrary Hom-modules as a generalization of Kac’s result.
基金The National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK20171348)
文摘Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,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)-pseudoalgebras.Finally,some examples of the(H,R)-pseudoalgebra are given explicitly,and the conditions for aHopf algebra to be an(H,R)-pseudoalgebra(resp.Hpseudoalgebra)are discussed.
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.
基金the grant of Guangzhou Civil Aviation College(Grant No.22X0430)the RAS Fundamental Research Program(Grant No.FWNF-2022-0002)+2 种基金the NNSF of China(Grant Nos.11571121,12071156)the NNSF of China(Grant No.12101248)the China Postdoctoral Science Foundation(Grant No.2021M691099)。
文摘In this article,we construct free centroid hom-associative algebras and free centroid hom-Lie algebras.We also construct some other relatively free centroid hom-associative algebras by applying the Gr?bner-Shirshov basis theory for(unital)centroid hom-associative algebras.Finally,we prove that the"Poincaré-Birkhoff-Witt theorem"holds for certain type of centroid hom-Lie algebras over a field of characteristic 0,namely,every centroid hom-Lie algebra such that the eigenvectors of the mapβlinearly generates the whole algebra can be embedded into its universal enveloping centroid hom-associative algebra,and the linear basis of the universal enveloping algebra does not depend on the multiplication table of the centroid hom-Lie algebra under consideration.
基金Supported by National Natural Science Foundation grants of China(Grant No.11301109)。
文摘On Hom-Lie algebras and superalgebras,we introduce the notions of biderivations and linear commuting maps,and compute them for some typical Hom-Lie algebras and superalgebras,including the q-deformed W(2,2)algebra,the q-deformed Witt algebra and superalgebra.
基金Supported by China Scholarship Council(Grant No.201206125047)China Postdoctoral Science Foundation Funded Project(Grant No.2012M520715)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.201462)
文摘This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W（2, 2） algebra. We show that the q-deformed W（2, 2） algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed W（2, 2） algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras.As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W（2, 2） algebra.
基金Supported by National Natural Science Foundation grants of China(Grant No.11301109)the Research Fund for the Doctoral Program of Higher Education(Grant No.20132302120042)
文摘The aim of this paper is to introduce and study Hom-Gel＇fand-Dorfman super-bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing Hom- Gel＇fand-Dorfman super-bialgebras. Also, we obtain some infinite-dimensional Hom-Lie superalgebras from affinization of Hom-Gel＇fand-Dorfman super-bialgebras. Finally, we give a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras and establish the equivalence between quadratic Hom-Lie conformal superalgebras and Hom-Gel＇fand-Dorfman super-bialgebras.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171055, 11471090 and 11301109)Natural Science Foundation of Jilin Province (Grant No. 20170101048JC)
文摘The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce α~k-derivations of multiplicative Hom-Lie conformal algebras and study their properties.
