共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper is a continuation of [EK]. We show that the quantization procedure of [EK] is given by universal acyclic formulas
and defines a functor from the category of Lie bialgebras to the category of quantized universal enveloping algebras. We
also show that this functor defines an equivalence between the category of Lie bialgebras over k [[h]] and the category of quantized universal enveloping (QUE) algebras. 相似文献
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We study the representations of the restricted two-parameter quantum groups of types B and G . For these restricted two-parameter quantum groups, we give some explicit conditions which guarantee that a simple module can be factored as the tensor product of a one-dimensional module with a module that is naturally a module for the quotient by central group-like elements. That is, given θ a primitive l th root of unity, the factorization of simple ? θ y , θ z , ( ) - modules is possible, if and only if (2(y - z ), l ) = 1 for = ? ? 2 n + 1 ; (3(y - z ), l ) = 1 for g= G 2. 相似文献
4.
Xiao Xia ZHANG 《数学学报(英文版)》2006,22(4):1221-1226
In this paper, we first prove that the θ-deformation Uθ(2) of U(2) constructed by Connes and Violette is our special case of the quantum group Uq(2) constructed in our previous paper. Then we will show that the set of truces on the C^* -algebra Uθ, θ irrational, is determined by the set of the truces on a subalgebra of Uθ. 相似文献
5.
Paul Gilmartin 《代数通讯》2019,47(7):2833-2842
Let k be a field and let H denote a pointed Hopf k-algebra with antipode S. We are interested in determining the order of S. Building on the work done by Taft and Wilson in [7], we define an invariant for H, denoted mH, and prove that the value of this invariant is connected to the order of S. In the case where char k?=?0, it is shown that if S has finite order then it is either the identity or has order 2?mH. If in addition H is assumed to be coradically graded, it is shown that the order of S is finite if and only if mH is finite. We also consider the case where char k?=?p?>?0, generalizing the results of [7] to the infinite-dimensional setting. 相似文献
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Derivations and Automorphisms of the Positive Part of the Two-parameter Quantum Group Ur,s(B3) 下载免费PDF全文
We compute the derivations of the positive part of the two-parameter quantum group U_(r,s)(B_3) and show that the Hochschild cohomology group of degree 1 of this algebra is a threedimensional vector space over the base field C. We also compute the groups of(Hopf) algebra automorphisms of the augmented two-parameter quantized enveloping algebra ?_(r,s)~(≥0)(B_3). 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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量子群的基变换与范畴同构 总被引:5,自引:1,他引:5
令M是Z[v]的由v-1和奇素数p生成的理想,U是A=Z[v]M上相伴于对称Cartan矩阵的量子群, A-Γ是环同态, Uг=UAΓ[Uг]是Uг的量子坐标代数,本文建立了量子坐标代数的基变换:即在相关约束条件下有Г-Hopf同构 A[U]AГ≌Г[Uг].我们证明了有限秩 A自由 1型可积 U模范畴和有限秩 A自由 A[U]余模范畴是同构的.特别,当 Г是域时,局部有限 1型 Uг模范畴和Г[Uг]余模范畴是同构的.最后,我们还证明了在[1]中定义的诱导函子和B.Parshall与王建磐博士在[2]中研究的诱导函子的一致性. 相似文献
12.
Naihong Hu 《代数通讯》2013,41(9):3202-3220
This article is the sequel to [11] to study the deformed structures and representations of two-parameter quantum groups U r, s (𝔤) associated to the finite dimensional simple Lie algebras 𝔤. An equivalence of the braided tensor categories 𝒪 r, s and 𝒪 q under the assumption rs ?1 = q 2 is explicitly established. 相似文献
13.
Diming Lu 《中国科学A辑(英文版)》1998,41(2):139-146
Let (H,R) be a triangular Hopf algebra. The monoidal functors on the category of representations ofH is studied, and a universal quantum commutative algebraSeR(M) and a dual H°-comoduleM° for any H-moduleM with an integrale are constructed. Both constructions given here have tensor isomorphism properties.
Project supported by the National Natural Science Foundation of China. 相似文献
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We provide a classification of finite-dimensional connected coradically graded pointed Majid algebras, generated in degrees 0 and 1, over the Klein group on the field of complex numbers. 相似文献
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一类量子环面李代数的自同构群 总被引:3,自引:0,他引:3
=C_q[x_1~(±1),x_2~(±1)]为复数域上的非交换环面结合代数,A=\C,Der为的导子李代数.本文研究李代数L_q=DerA的自同构群Aut L_q. 相似文献
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Yu. A. Chapovsky A. A. Kalyuzhnyi G. B. Podkolzin 《Functional Analysis and Its Applications》2006,40(2):139-142
We obtain an explicit formula for finding cocycles on a matched pair of Lie groups by using cocycles on the corresponding pair of Lie algebras. This formula for cocycles allows one to construct examples of locally compact quantum groups via bicrossproduct of Lie groups. 相似文献
18.
We classify the orbits of coquasi-triangular structures for the Hopf algebra E(n) under the action of lazy cocycles and the Hopf automorphism group. This is applied to detect subgroups of the Brauer group BQ(k,E(n)) of E(n) that are isomorphic. For any triangular structure R on E(n) we prove that the subgroup BM(k,E(n),R) of BQ(k,E(n)) arising from R is isomorphic to a direct product of BW(k), the Brauer-Wall group of the ground field k, and Symn(k), the group of n × n symmetric matrices under addition. For a general quasi-triangular structure R on E(n) we construct a split short exact sequence having BM(k,E(n),R) as a middle term and as kernel a central extension of the group of symmetric matrices of order r < n (r depending on R). We finally describe how the image of the Hopf automorphism group inside BQ(k,E(n)) acts on Symn (k). 相似文献
19.
We investigate a connection between distance-regular graphs and U
q(sl(2)), the quantum universal enveloping algebra of the Lie algebra sl(2). Let be a distance-regular graph with diameter d 3 and valency k 3, and assume is not isomorphic to the d-cube. Fix a vertex x of , and let
(x) denote the Terwilliger algebra of with respect to x. Fix any complex number q {0, 1, –1}. Then
is generated by certain matrices satisfying the defining relations of U
q(sl(2)) if and only if is bipartite and 2-homogeneous. 相似文献
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