We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of c...We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Poisson color algebras A is of the form A = U +Σα Iα with U a subspace of a maximal abelian subalgebra H and any Iα , a well described ideal of A, satisfying [Iα,Iβ]+ IαIβ= 0 if [α]≠[β]. Under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized.展开更多
The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the h...The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.展开更多
In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some ...In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.展开更多
In this paper,we introduce the representation and cohomology theory of Lie-Yamaguti color algebras.Furthermore,we introduce the notions of generalized derivations of Lie-Yamaguti color algebras and present some proper...In this paper,we introduce the representation and cohomology theory of Lie-Yamaguti color algebras.Furthermore,we introduce the notions of generalized derivations of Lie-Yamaguti color algebras and present some properties.Finally,we study linear deformations of LieYamaguti color algebras,and introduce the notion of a Nijenhuis operator on a Lie-Yamaguti color algebra,which can generate a trivial deformation.展开更多
We investigate the colored Yang–Baxter equation. Based on a trigonometric solution of colored Yang–Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and hi...We investigate the colored Yang–Baxter equation. Based on a trigonometric solution of colored Yang–Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.展开更多
We prove that each finitely generated (as a module) complete color Lie superalgebras over noetherian ring can be decomposed uniquely into a direct sum of complete simple ideals.
基金Supported by the National Natural Science Foundation of China(Grant No.11761017)the Youth Project for Natural Science Foundation of Guizhou Provincial Department of Education(Grant No.KY[2018]155)
文摘We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Poisson color algebras A is of the form A = U +Σα Iα with U a subspace of a maximal abelian subalgebra H and any Iα , a well described ideal of A, satisfying [Iα,Iβ]+ IαIβ= 0 if [α]≠[β]. Under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized.
基金The Natural Science Foundation of Jiangsu Province(No.BK2012736)the Natural Science Foundation of Chuzhou University(No.2010kj006Z)
文摘The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.
基金National Natural Science Foundation of China(10271076)
文摘In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.
基金Supported by the National Natural Science of China(Grant No.11761017)the Science and Technology Foundation of Guizhou Province(Grant No.[2020]1Y005)。
文摘In this paper,we introduce the representation and cohomology theory of Lie-Yamaguti color algebras.Furthermore,we introduce the notions of generalized derivations of Lie-Yamaguti color algebras and present some properties.Finally,we study linear deformations of LieYamaguti color algebras,and introduce the notion of a Nijenhuis operator on a Lie-Yamaguti color algebra,which can generate a trivial deformation.
基金Supported by National Natural Science Foundation of China under Grant Nos.11171329,11375119,and 11031005Beijing Municipal Commission of Education under Grant No.KZ201210028032
文摘We investigate the colored Yang–Baxter equation. Based on a trigonometric solution of colored Yang–Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.
文摘We prove that each finitely generated (as a module) complete color Lie superalgebras over noetherian ring can be decomposed uniquely into a direct sum of complete simple ideals.
基金Supported by NNSF of China (11801121)NSF of Heilongjiang province(QC2018006)the Fundamental Research Fundation for Universities of Heilongjiang Province(LGYC2018JC002)。
