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
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
In this paper, we study one parameter deformation of full symmetric Toda hierarchy. This deformation is induced by Hom-Lie algebras, or is the applications of Hom-Lie algebras. We mainly consider three kinds of deform...In this paper, we study one parameter deformation of full symmetric Toda hierarchy. This deformation is induced by Hom-Lie algebras, or is the applications of Hom-Lie algebras. We mainly consider three kinds of deformation, and give solutions to deformations respectively under some conditions.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
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.
基金National Natural Science Foundation of China(11071187)Natural Science Foundation of Henan Prouince(11230041015)Education Department of Henan Province(2011A110022)
基金The Science and Technology Project(GJJ161029) of Department of Education,Jiangxi Province
文摘In this paper, we study one parameter deformation of full symmetric Toda hierarchy. This deformation is induced by Hom-Lie algebras, or is the applications of Hom-Lie algebras. We mainly consider three kinds of deformation, and give solutions to deformations respectively under some conditions.
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.
