量子包络代数Uq（sl2）的代数自同构

令Ｕｑ表示一个有限维单李代数ψ的普遍包络代数的量子化。文献「１」描述了代数Ｕｑ（ψ）的所有Ｈｏｐｆ－代数自同构。文献「２」确定Ｕｑ（ψ）的所有变形代数自同构，所谓变形代数自同构是指底下的单李代数ψ的自同构的形变。文中将确定代数Ｕｑ（ｓｌ２）的所有代数自同构。从而表明Ｕｑ（ｓｌ２）的所有代数自同构都是变形代数自同构。     

量子群中的Coxeter变换的"阶"

设g是有限维复单李代数.本文考虑量子群Uq(g)中两个特殊的自同构及它们作用在Uq(g)上及其可积Uq(g)-模上的性态.     

利用Uq(sp(8))的向量表示实现辛型量子群(O)(Spq(8))

Jantzen[1]利用A型李代数A2的量子包络代数Uq(sl2(C)),借助于其表示论并利用R-矩阵的方法给出了SLq(2)的定义关系式.本文对结构更为复杂的C型李代数做了类似的研究,通过Uq(sp(8))的表示理论实现了(O)(Spq(8))的定义关系式.     

量子群Uq(D4)上不可约模的Grobner-Shirshov对

首先,利用量子群Uq (D4)的已知的Grobner-Shirshov基和Chibrikov的双自由模方法来计算量子群Uq(D4)上不可约模Vq(λ)的一个Grobner-Shirshov对,然后在Uq(D4)的适当形式U'q(D4)中取q=1得到D4型单李代数的泛包络代数U(D4)上不可约模V(λ)的一个Grobner-Shirshov对.     

Multi-proxy quantum group signature scheme with threshold shared verification

A multi-proxy quantum group signature scheme with threshold shared verification is proposed. An original signer may authorize a proxy group as his proxy agent. Then only the cooperation of all the signers in the proxy group can generate the proxy signature on behalf of the original signer. In the scheme, any t or more of n receivers can verify the message and any t - 1 or fewer receivers cannot verify the validity of the proxy signature.     

量子群有限维表示的好滤过和循环模

证明了量子群有限维表示具有好滤过的上同调条件；给出了秩１量子群关于ＵｂΓ循环模的结构     

Categorification of integrable representations of quantum groups

We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac–Moody algebra. As a byproduct, we obtain a geometric realization of Lusztig's canonical bases of these representations as well as a new positivity result. The main ingredient in the underlying geometric construction is a class of micro-local perverse sheaves on quiver varieties.     

量子群U_q(sl(2 ) )的非负部分(英文)

设U≥ 0 是量子群Uq(sl(2 ) )的非负部分 .在本文中 ,我们确定了U≥ 0 的中心Z(U≥ 0 )和U≥ 0 的所有不可约表示     

关于双参数量子群的注记(I)

借助于Euler型, 给出了一类(对应于半单Lie代数的)双参数量子群的更为简便的定义方式, 证明了所定义量子群的正部分在双参数满足适当条件下是互为2-上圈形变的, 并给出了该正部分 在Kashiwara意义下的斜微分算子实现.     

Generalized Quantum Current Algebras

Two general families of new quantum-deformed current algebras are proposed and identified both as infinite Hopf family of algebras ,a structure which enables one to define “Tensor products“ of these algebras.The standard quantum affine algebras turn out to be a very special case of the two algebra families,in which case the infinite Hopt family structure degenerates into a standard Hopf algebra.The relationship between the two algebraic families as well as their various special examples are discussed,and the free boson representation is also considered.