量子群Uq(sl(2))中理想的唯一分解

本文利用量子群Uq(sl(2))的表示及其理想的生成子,证明了Uq(sl(2))的任一非零理想在某种意义下可唯一分解为若干个素理想的乘积.由此得到理想的求根公式.     

量子群${\cal U}_q(\osp(1,2,f))$的结构

In this paper we construct a new quantum group Uq（osp（1,2,f））,which can be seen as a generalization of Uq（osp（1,2））.A necessary and sufficient condition for the algebra Uq（osp（1,2,f）） to be a super Hopf algebra is obtained and the center Z（Uq（osp（1,2,f））） is given.     

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.     

Young表与Uq（osp（1｜2n））的晶体基

设Uq（osp（1｜2n））是对应Lie超代数osp（1｜2n）的量子包络超代数．利用满足一定条件的半标准Young表,给出有限维既约Uq（osp（1｜2n））模晶体图的实现．建立晶体图张量积分解的广义Littlewood—Richardson法则．     

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.     

量子群Uq（sl（2））的非负部分

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

量子仿射李超代数Uq(osp(2n+1|2m)(1))的Serre关系

osp(2n+1|2m)⁽⁽¹⁾)是一类非常重要的仿射李代数.其结构不仅含有Serre关系,而且还有高阶Serre关系.本文给出了量子仿射李超代数U_q(osp(2n+1|2m)((1))是一类非常重要的仿射李代数.其结构不仅含有Serre关系,而且还有高阶Serre关系.本文给出了量子仿射李超代数U_q(osp(2n+1|2m)⁽⁽¹⁾))所有Serre关系的详细表达式,对研究该李超代数和量子超代数的表示有着积极的作用.     

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     

Young表与$\textrm{U}_{q}(\mathrm{osp}(1|2n))$的晶体基

设 $U_q(\mathrm{osp}(1|2n))$是对应Lie超代数$\mathrm{osp}(1|2n)$的量子包络超代数. 利用满足一定条件的半标准Young表, 给出有限维既约$U_q(\mathrm{osp}(1|2n))$模晶体图的实现 . 建立晶体图张量积分解的广义Littlewood-Richardson法则.     

Smash积为超限左自由正规化扩张的充分条件及其应用

本文给出了代数A与双代数H的Smash积AH是A的超限左自由正规化扩张的一个充分条件．进一步,主要结果被运用到斜半群环、斜群环和量子群Uq（sl（2））从而给出了它们的一些性质．     

The Structure of Quantum Group Uq(osp(1, 2, f))

In this paper we construct a new quantum group Uq(osp(1,2, f)), which can be seen as a generalization of Uq(oSp(1, 2)). A necessary and sufficient condition for the algebra Uq(oSp(1,2, f)) to be a super Hopf algebra is obtained and the center Z(Uq(osp(1,2, f))) is given.     

路余代数上的Hopf ε-代数

在q不为单位根时，本文用无限简图A∞∞的double路余代数KA∞∞^—的商代数同时实现了量子代数Uq（sl2）以及量子超代数Uq（ops（2，1））．     

The Zhang Transformation and U q (osp(1,2l))-Verma Modules Annihilators

R. B. Zhang found a way to link certain formal deformations of the Lie algebra o(2l+1) and the Lie superalgebra osp(1,2l). The aim of this article is to reformulate the Zhang transformation in the context of the quantum enveloping algebras à la Drinfeld and Jimbo and to show how this construction can explain the main theorem of Gorelik and Lanzmann: the annihilator of a Verma module over the Lie superalgebra osp(1,2l) is generated by its intersection with the centralizer of the even part of the enveloping algebra.     

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...     

Young tableaux and crystal base for U_q(osp(1|2n))

Let Uq(osp(1|2n)) be the quantized enveloping superalgebra corresponding to the Lie superalgebra osp(1|2n). In terms of semistandard Young tableaux satisfying some additional conditions, a realization of crystal graph of finite-dimensional irreducible modules of Uq(osp(1|2n)) is given. Also, the generalized LittlewoodRichardson rule for tensor product of crystal graphs is established.     

Quantum Weyl symmetric polynomials and the center of quantum group U_q(sl_4)

Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.     

The annihilation theorem for the completely reducible Lie superalgebras

A well known theorem of Duflo claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is generated by its intersection with the centre. For a Lie superalgebra this result fails to be true. For instance, in the case of the orthosymplectic Lie superalgebra osp(1,2), Pinczon gave in [Pi] an example of a Verma module whose annihilator is not generated by its intersection with the centre of universal enveloping algebra. More generally, Musson produced in [Mu1] a family of such “singular” Verma modules for osp(1,2l) cases. In this article we give a necessary and sufficient condition on the highest weight of a osp(1,2l)-Verma module for its annihilator to be generated by its intersection with the centre. This answers a question of Musson. The classical proof of the Duflo theorem is based on a deep result of Kostant which uses some delicate algebraic geometry reasonings. Unfortunately these arguments can not be reproduced in the quantum and super cases. This obstruction forced Joseph and Letzter, in their work on the quantum case (see [JL]), to find an alternativeapproach to the Duflo theorem. Following their ideas, we compute the factorization of the Parthasarathy–Ranga-Rao–Varadarajan (PRV) determinants. Comparing it with the factorization of Shapovalov determinants we find, unlike to the classical and quantum cases, that the PRV determinant contains some extrafactors. The set of zeroes of these extrafactors is precisely the set of highest weights of Verma modules whose annihilators are not generated by their intersection with the centre. We also find an analogue of Hesselink formula (see [He]) giving the multiplicity of every simple finite dimensional module in the graded component of the harmonic space in the symmetric algebra. Oblatum 1-IX-1998 & 4-XII-1998 / Published online: 10 May 1999     

量子群V_q(sl(2))的商代数

本文研究当q是单位根时,V_q(sl(2))在关系H~r=K~r=1,E~(mr)=F~(nr)=0下的商代数V_q(m,n)的构造与分解,以及它的区块结构.为此,首先将U_q(sl(2))的基本性质和重要结论推广到V_q(sl(2)),并研究V_q(sl(2))的模的基本性质.利用这些结论,我们逐步构造出V_q(m,n)的左理想,并将V_q(m,n)分解成不可分解的左理想的直和.然后,把V_q(m,n)的不可分解的左理想合并成区块,并研究区块结构,从而把V_q(m,n)的表示问题归结成一个代数表示论的问题.