In order to study the deformation of algebras the notions of Hom-algebras are introduced.The Hom-algebra is a generalization of the classical associative algebra.First the Hom-type generalization of dimodules which is...In order to study the deformation of algebras the notions of Hom-algebras are introduced.The Hom-algebra is a generalization of the classical associative algebra.First the Hom-type generalization of dimodules which is called the Hom-dimodule is introduced and its properties are discussed Moreover the category of Hom-dimodules in connection with the Hom D-equation R12 R23 =R23 R12 for R∈Endk M⊙M and a Hom-module M is investigated.Some solutions of the Hom D-equation from Hom-dimodules over Hom-bialgebras are given and the FRT-type theorem is constructed in the category of Hom-dimodules. The results generalize and improve the FRT-type theorem in the category of dimodules.展开更多
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
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
基金The National Natural Science Foundation of China(No.11371089)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)the Postdoctoral Innovation Funds of Southeast University(No.3207013601)
文摘In order to study the deformation of algebras the notions of Hom-algebras are introduced.The Hom-algebra is a generalization of the classical associative algebra.First the Hom-type generalization of dimodules which is called the Hom-dimodule is introduced and its properties are discussed Moreover the category of Hom-dimodules in connection with the Hom D-equation R12 R23 =R23 R12 for R∈Endk M⊙M and a Hom-module M is investigated.Some solutions of the Hom D-equation from Hom-dimodules over Hom-bialgebras are given and the FRT-type theorem is constructed in the category of Hom-dimodules. The results generalize and improve the FRT-type theorem in the category of dimodules.
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.
