共查询到18条相似文献,搜索用时 240 毫秒
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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. 相似文献
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量子群Uq(sl(2))中理想的唯一分解 总被引:1,自引:0,他引:1
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. 相似文献
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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. 相似文献
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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. 相似文献
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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。 相似文献
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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. 相似文献
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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 相似文献
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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. 相似文献
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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)). 相似文献
13.
Emmanuel Lanzmann 《Algebras and Representation Theory》2002,5(3):235-258
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. 相似文献
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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 相似文献
15.
Kristien Bauwens 《代数通讯》2013,41(11):4405-4415
The homogenization of a superenveloping algebra is Auslander regular iff this enveloping algebra is a domain. This note determines points and lines in the quantum space of the homogenized envelope of the classical simple Lie superalgebra osp(l,2). It is also concerned with homogenized sl(2), which is graded embedded in homogenized osp(l,2), and describes the conies in the associated quantum space. 相似文献
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Zhi Hua WANG Li Bin LI .School of Mathematics Yangzhou University Jiangsu P.R.China 《数学研究与评论》2011,(4)
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... 相似文献
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LIU JunLi & YANG ShiLin College of Applied Sciences Beijing University of Technology Beijing China 《中国科学 数学(英文版)》2010,(2)
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. 相似文献
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The aim of this paper is to study the adjoint action for the quantum algebra Uq(f(K, H)), which is a natural generalization of quantum algebra Uq(sl2) and is regarded as a class of generalized Weyl algebra..The structure theorem of its locally finite subalgebra F(Uq(f(K, H))) is given. 相似文献