Structural mapping is an important method for studying algebraic structures.Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings,respectively.These structures are imp...Structural mapping is an important method for studying algebraic structures.Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings,respectively.These structures are important algebra and group generalizations and are closely related to them.Let(A,β)be a Hom-algebra and(G,α)a monoidal Hom-group.A structure of(A,β)graded by(G,α)is introduced;this structure is called Hom-group graded algebra.This study presents the definition of Hom group graded algebra,provides some examples,and dis-cusses its basic properties.Furthermore,a sufficient and necessary condition that makes(A,β)a strongly(G,α)-graded algebra is explored using a structure mapβand unit 1A.Finally,by using different maps,two sufficient and necessary conditions for a Hom-algebra to be a(G,α)-graded algebra are expressed in different ways.展开更多
A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map.In this paper,we give some new examples of Hom-groups,and show the first,second ...A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map.In this paper,we give some new examples of Hom-groups,and show the first,second and third isomorphism theorems of Hom-groups.We also introduce the notion of Hom-group action,and as an application,we prove the first Sylow theorem for Hom-groups along the line of group actions.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 National Natural Science Foundation of China (No. 12271089, 12471033)。
文摘Structural mapping is an important method for studying algebraic structures.Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings,respectively.These structures are important algebra and group generalizations and are closely related to them.Let(A,β)be a Hom-algebra and(G,α)a monoidal Hom-group.A structure of(A,β)graded by(G,α)is introduced;this structure is called Hom-group graded algebra.This study presents the definition of Hom group graded algebra,provides some examples,and dis-cusses its basic properties.Furthermore,a sufficient and necessary condition that makes(A,β)a strongly(G,α)-graded algebra is explored using a structure mapβand unit 1A.Finally,by using different maps,two sufficient and necessary conditions for a Hom-algebra to be a(G,α)-graded algebra are expressed in different ways.
基金Supported by NSF of Jilin Province(Grant No.YDZJ202201ZYTS589)NNSF of China(Grant Nos.12271085,12071405)the Fundamental Research Funds for the Central Universities。
文摘A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map.In this paper,we give some new examples of Hom-groups,and show the first,second and third isomorphism theorems of Hom-groups.We also introduce the notion of Hom-group action,and as an application,we prove the first Sylow theorem for Hom-groups along the line of group actions.
基金supported by the National Science Foundation of China(11047030)Natural Science Foundation of Henan Provincial Eduction Department(2010B110003)Natural Science Foundation of Henan University(2009YBZR025)
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.
