Action of μq(g) on Its Positive Part μq+(g)

In this paper,two kinds of skew derivations of a type of Nichols algebras are introduced,and then the relationship between them is investigated.In particular they satisfy the quantum Serre-relations.Therefore,the algebra generated by these derivations and corresponding automorphisms is a homomorphic image of the Drinfeld-Jimbo quantum enveloping algebra μq(g),which proves the Nichols algebra becomes aμq(g)-module algebra.But the Nichols algebra considered here is exactly μq+(g),namely,the positive part of the Drinfeld-Jimbo quantum enveloping algebra μq(g),it turns out that μq+(g)is a μq(g)-module algebra.     

关于$omega$-Smash余积Hopf代数的$(f,omega)$相容对$(B,,H)$

In this paper we introduce the notion of （f,ω）-compatible pair （B,H）, by which we construct a Hopf algebra in the category HHYD of Yetter-Drinfeld H-modules by twisting the comultiplication of B. We also study the property of ω-smash coproduct Hopf algebras Bω H.     

Action of U_q(g) on Its Positive Part U_q~+(g)

In this paper,two kinds of skew derivations of a type of Nichols algebras are intro- duced,and then the relationship between them is investigated.In particular they satisfy the quantum Serre relations.Therefore,the algebra generated by these derivations and correspond- ing automorphisms is a homomorphic image of the Drinfeld-Jimbo quantum enveloping algebra U q (g),which proves the Nichols algebra becomes a U q (g)-module algebra.But the Nichols alge- bra considered here is exactly U + q (g),namely,the posi...     

Construction of Rota-Baxter algebras via Hopf module algebras

We propose the notion of Hopf module algebra and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight-1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld module algebras. As an application,we prove that the positive part of a quantum group admits idempotent Rota-Baxter algebra structures.     

弱Hopf群T-余代数上的弱Doi-Hopf群模

在弱Hopf群T-余代数情形下,弱量子Yetter-Drinfeld群模的概念被引入,并证明了弱量子Yetter-Drinfeld群模是特殊的弱Doi-Hopf群模.接着建立了弱量子Yetter Drinfeld群模范畴与弱Hopf群双余模代数的余不动点子代数B上模范畴之间的伴随对.最后考虑了弱量子Yetter-Drinfeld群模的积分.     

T-余代数上的Yetter-Drinfeld模范畴

研究T-余代数上的Yetter-Drinfeld模的各种性质.设π是一个群,H是T-余代数,对任意的α∈π,则有范畴α-HyDH.设M∈α-HyDH,N∈β-HyDH,证明了M N∈αβ-HyDH;若β∈π,则βM∈βαβ-1-HyDH,从而使HyDH成为T-范畴.构造了HyDH的一个辫结构使得它是辫子张量T-范畴.     

Hopf modules and the double of a quasi-Hopf algebra

We give a different proof for a structure theorem of Hausser and Nill on Hopf modules over quasi-Hopf algebras. We extend the structure theorem to a classification of two-sided two-cosided Hopf modules by Yetter-Drinfeld modules, which can be defined in two rather different manners for the quasi-Hopf case. The category equivalence between Hopf modules and Yetter-Drinfeld modules leads to a new construction of the Drinfeld double of a quasi-Hopf algebra, as proposed by Majid and constructed by Hausser and Nill.