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1.
Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q(g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q(g,Λ) and U = U_q(g,Q). 相似文献
2.
定义了sl_2一种新的量子代数U_q(sl_2,C),它是U_q(sl_2)的推广.设(U_q(sl_2,C))(≥0)是U_q(sl_2,C)的非负部分,刻画了(U_q(sl_2,C))(≥0)是U_q(sl_2,C)的非负部分,刻画了(U_q(sl_2,C))(≥0)的中心,(U_q(sl_2,C))(≥0)的中心,(U_q(sl_2,C))(≥0)上的所有有限维不可约表示以及单位根时U_q(sl_2,C)的中心. 相似文献
3.
主要讨论一阶量子广义Kac-Moody代数U_q(2α)的结构,其中a∈Z0.在此基础上,刻画了量子广义代数U_q(g)的另一种整形式. 相似文献
4.
Both in Majid's double-bosonization theory and in Rosso's quantum shuffle theory, the rankinductive and type-crossing construction for U_q(g)'s is still a remaining open question. In this paper, working in Majid's framework, based on the generalized double-bosonization theorem we proved before, we further describe explicitly the type-crossing construction of U_q(g)'s for(BCD)_n series directly from type An-1via adding a pair of dual braided groups determined by a pair of(R, R′)-matrices of type A derived from the respective suitably chosen representations. Combining with our results of the first three papers of this series, this solves Majid's conjecture, i.e., any quantum group U_q(g) associated to a simple Lie algebra g can be grown out of U_q(sl_2)recursively by a series of suitably chosen double-bosonization procedures. 相似文献
5.
设H是Hopf代数,g是由Cartan矩阵A=(a_(ij))_(I×I)决定的广义Kac-Moody代数,这里的I是指标集,它或者是有限个整数{1,2,…,n},或者是整个自然数集N,用f,g表示从I到Hopf代数H的群象元素集G(H)两个映射,假如集合{f(i),g(i)|i∈I}中任何两个元素乘法可以交换,则可以在H(?)_g~f U_q(g)上定义一种Hopf结构,这里的U_q(g)是g量子包络代数. 相似文献
6.
《数学的实践与认识》2021,(1)
首先,利用量子群U_q (D_4)的已知的Gr?bner-Shirshov基和Chibrikov的双自由模方法来计算量子群U_q(D_4)上不可约模V_q(λ)的一个Gr?bner-Shirshov对,然后在U_q(D_4)的适当形式U'_q(D_4)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Gr?bner-Shirshov对. 相似文献
7.
利用量子群U=U_q(f(K))的表示理论及其局部有限子代数F(U)的子模结构,证明了U_q(f(K))的局部有限子代数F(U)的任一非零理想均可由若干个具有不同权的最高权向量的和生成. 相似文献
8.
First, the authors give a Grbner-Shirshov basis of the finite-dimensional irreducible module Vq(λ) of the Drinfeld-Jimbo quantum group U_q(G_2) by using the double free module method and the known Grbner-Shirshov basis of U_q(G_2). Then, by specializing a suitable version of U_q(G_2) at q = 1, they get a Grbner-Shirshov basis of the universal enveloping algebra U(G_2) of the simple Lie algebra of type G_2 and the finite-dimensional irreducible U(G_2)-module V(λ). 相似文献
9.
A two-parameter quantum group is obtained from the usual enveloping algebra by adding two commutative grouplike elements. In this paper, we generalize this procession further by adding commutative grouplike elements b_(ik), c_(ik), g_(ik), h_(ik)(i ∈I, k = 1,..., mi) of a Hopf algebra H to the quantized enveloping algebra U_q(G) of a Borcherds superalgebra G defined by a symmetrizable integral Borcherds–Cartan matrix A =(aij)i,j∈I. Therefore, we define an extended Hopf superalgebra HU_q(G). We also discuss the basis and the grouplike elements of HU_q(G). 相似文献
10.
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
11.
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
12.
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.
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
14.
设Vm是量子群Uq(SLm)的标准表示,通过Hecke代数的作用,作者将Vm的张量积V^nm分解成了Uq(SLm)的不可约表示的直和,从而给出了Uq(SLm)与Hecke代数的H(q,n)Schur-Weyl对偶的完整证明,进一步得到,当q是实数时,在Hilbert空间H^n上,Uq(SL∞)和H(q,n)之间存在着Schur-Weyl对偶。 相似文献
15.
PAUL G.A. FLORIS 《Compositio Mathematica》1997,108(2):123-149
Abstract. Explicit models are constructed for irreducible *-representations of the quantised universalenveloping algebra Uq(gl(n)). The irreducible decomposition of these modules with respect to thesubalgebra Uq(gl(n-1)) is given, and the corresponding spherical and associated spherical elementsare determined in terms of little q-Jacobi polynomials. This leads to a proof of an addition theoremfor the spherical elements, the so-called q-disk polynomials. 相似文献
16.
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
17.
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
18.
TOSHIKI NAKASHIMA 《Compositio Mathematica》1997,108(1):1-33
Crystal base of the level 0 part of the modified quantum affine algebra Uq(sl2)_0 is given by path. Weyl group actions, extremal vectors and crystal structure of all irreducible components are described explicitly. 相似文献
19.
WU JingYan WEI JunChao & LI LiBin School of Mathematics Yangzhou University Yangzhou China Shijiazhuang Experimental Middle School Shijiazhuang 《中国科学 数学(英文版)》2011,(1)
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. 相似文献
20.
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