In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction ...In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and nonco- commutative Hopf algebras.展开更多
In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra H.Although the category of all left H-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Dri...In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra H.Although the category of all left H-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra H, and a series of weak Hopf algebras. Some results of [8] are generalized.展开更多
Suppose that H is a Hopf algebra,and g is a generalized Kac-Moody algebra with Cartan matrix A=(aij)I×I,where I is an index set and is equal to either{1,2,...,n}or the natural number set N.Let f,g be two mappings...Suppose that H is a Hopf algebra,and g is a generalized Kac-Moody algebra with Cartan matrix A=(aij)I×I,where I is an index set and is equal to either{1,2,...,n}or the natural number set N.Let f,g be two mappings from I to G(H),the set of group-like elements of H,such that the multiplication of elements in the set{f(i),g(i)|i∈I}is commutative.Then we define a Hopf algebra Hgf Uq(g),where Uq(g)is the quantized enveloping algebra of g.展开更多
基金Supported by Zhejiang Provincial Natural Science Foundation of China(Y6100148,Y610027)Education Department of Zhejiang Province(201019063)National Natural Science Foundation of China(11171296)
文摘In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and nonco- commutative Hopf algebras.
基金Supported by ZJNSF(LY17A010015,LZ14A010001)NNSF(11171296),CSC
文摘In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra H.Although the category of all left H-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra H, and a series of weak Hopf algebras. Some results of [8] are generalized.
基金supported by Zhejiang Natural Science Foundation(Grant No.Y607136)
文摘Suppose that H is a Hopf algebra,and g is a generalized Kac-Moody algebra with Cartan matrix A=(aij)I×I,where I is an index set and is equal to either{1,2,...,n}or the natural number set N.Let f,g be two mappings from I to G(H),the set of group-like elements of H,such that the multiplication of elements in the set{f(i),g(i)|i∈I}is commutative.Then we define a Hopf algebra Hgf Uq(g),where Uq(g)is the quantized enveloping algebra of g.
