Let H be a Hopf algebra and HYD the Yetter- Drinfeld category over H. First, the enveloping algebra of generalized H-Hom-Lie algebra L, i.e., Hom-Lie algebra L H in the category HYD, is constructed. Secondly, it is o...Let H be a Hopf algebra and HYD the Yetter- Drinfeld category over H. First, the enveloping algebra of generalized H-Hom-Lie algebra L, i.e., Hom-Lie algebra L H in the category HYD, is constructed. Secondly, it is obtained that U(L) = T( L)/L where I is the Hom-ideal of T(L) generated by {ll'-l_((-1))·l'l_0-[l,l']|l,l'∈L}, and u: L,T(L)/I is the canonical map. Finally, as the applications of the result, the enveloping algebras of generalized H-Lie algebras, i.e., the Lie algebras in the category MyDn and the Hom-Lie algebras in the category of left H-comodules are presented, respectively.展开更多
Let (C, C) be a braided monoidal category. The relationship between the braided Lie algebra and the left Jacobi braided Lie algebra in the category (C, C) is investigated. First, a braided C2-commutative algebra i...Let (C, C) be a braided monoidal category. The relationship between the braided Lie algebra and the left Jacobi braided Lie algebra in the category (C, C) is investigated. First, a braided C2-commutative algebra in the category (C, C) is defined and three equations on the braiding in the category (C, C) are proved. Secondly, it is verified that (A, [, ] ) is a left (strict) Jacobi braided Lie algebra if and only if (A, [, ] ) is a braided Lie algebra, where A is an associative algebra in the category (C, C). Finally, as an application, the structures of braided Lie algebras are given in the category of Yetter-Drinfel'd modules and the category of Hopf bimodules.展开更多
基金The National Natural Science Foundation of China(No.11371088)the Excellent Young Talents Fund of Anhui Province(No.2013SQRL092ZD)+2 种基金the Natural Science Foundation of Higher Education Institutions of Anhui Province(No.KJ2015A294)China Postdoctoral Science Foundation(No.2015M571725)the Excellent Young Talents Fund of Chuzhou University(No.2013RC001)
文摘Let H be a Hopf algebra and HYD the Yetter- Drinfeld category over H. First, the enveloping algebra of generalized H-Hom-Lie algebra L, i.e., Hom-Lie algebra L H in the category HYD, is constructed. Secondly, it is obtained that U(L) = T( L)/L where I is the Hom-ideal of T(L) generated by {ll'-l_((-1))·l'l_0-[l,l']|l,l'∈L}, and u: L,T(L)/I is the canonical map. Finally, as the applications of the result, the enveloping algebras of generalized H-Lie algebras, i.e., the Lie algebras in the category MyDn and the Hom-Lie algebras in the category of left H-comodules are presented, respectively.
基金The National Natural Science Foundation of China(No.10871042)
文摘Let (C, C) be a braided monoidal category. The relationship between the braided Lie algebra and the left Jacobi braided Lie algebra in the category (C, C) is investigated. First, a braided C2-commutative algebra in the category (C, C) is defined and three equations on the braiding in the category (C, C) are proved. Secondly, it is verified that (A, [, ] ) is a left (strict) Jacobi braided Lie algebra if and only if (A, [, ] ) is a braided Lie algebra, where A is an associative algebra in the category (C, C). Finally, as an application, the structures of braided Lie algebras are given in the category of Yetter-Drinfel'd modules and the category of Hopf bimodules.