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 do...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.展开更多
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
基金Supported by the National Natural Science Foundation of China(Grant Nos.11761017,11801150)the Science and Technology Foundation of Guizhou Province(Grant No.20201Y005)。
文摘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.
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National Natural Science Foundation of China(11071187)Natural Science Foundation of Henan Prouince(11230041015)Education Department of Henan Province(2011A110022)
基金Supported by the NNSF of China(11426095)the Foundation of Henan Educational Committee(14B110003)+3 种基金the NSF of Henan Province(152300410086)the Research Fund of PhD(qd14151)the Chuzhou University Excellent Young Talents Fund Project(2013RC001)the NSF of Chuzhou University(2014PY08)
