共查询到20条相似文献,搜索用时 15 毫秒
1.
A complete classification is given of all inner actions on the Clifford algebra C(l,3) defined by representations of the quantum group GLq (2,C)qm ≠1, which are not reduced to representations of two commuting “q-spinors”. As a consequence of this classification it is shown that the space of invariants of every GLq (2,C)-action of this type, which is not an action of SLq (2,C), is generatedby 1 and the value of the quantum determinant for the given representation. 相似文献
2.
A. K. Kwaśniewski 《Advances in Applied Clifford Algebras》1999,9(2):249-260
The non commuting matrix elements of matrices from quantum groupGL
q
(2;C) withq≡ω being then-th root of unity are given a representation as operators in Hilbert space with help ofC
4
(n)
generalized Clifford algebra generators appropriately tensored with unit 2×2 matrix infinitely many times. Specific properties
of such a representation are presented. Relevance of generalized Pauli algebra to azimuthal quantization of angular momentum
alà Lévy-Leblond [10] and to polar decomposition ofSU
q
(2;C) quantum algebra alà Chaichian and Ellinas [6] is also commented.
The case ofq∈C, |q|=1 may be treated parallely. 相似文献
3.
Wang Heping 《Journal of Mathematical Analysis and Applications》2007,335(2):1360-1373
In this paper, we discuss properties of convergence for the q-Meyer-König and Zeller operators Mn,q. Based on an explicit expression for Mn,q(t2,x) in terms of q-hypergeometric series, we show that for qn∈(0,1], the sequence (Mn,qn(f))n?1 converges to f uniformly on [0,1] for each f∈C[0,1] if and only if limn→∞qn=1. For fixed q∈(0,1), we prove that the sequence (Mn,q(f)) converges for each f∈C[0,1] and obtain the estimates for the rate of convergence of (Mn,q(f)) by the modulus of continuity of f, and the estimates are sharp in the sense of order for Lipschitz continuous functions. We also give explicit formulas of Voronovskaya type for the q-Meyer-König and Zeller operators for fixed 0<q<1. If 0<q<1, f∈C1[0,1], we show that the rate of convergence for the Meyer-König and Zeller operators is o(qn) if and only if
4.
Teodor Banica 《Journal of Functional Analysis》2011,260(11):3252-3282
We introduce and study natural two-parameter families of quantum groups motivated on one hand by the liberations of classical orthogonal groups and on the other by quantum isometry groups of the duals of the free groups. Specifically, for each pair (p,q) of non-negative integers we define and investigate quantum groups O+(p,q), B+(p,q), S+(p,q) and H+(p,q) corresponding to, respectively, orthogonal groups, bistochastic groups, symmetric groups and hyperoctahedral groups. In the first three cases the new quantum groups turn out to be related to the (dual free products of ) free quantum groups studied earlier. For H+(p,q) the situation is different and we show that , where the latter can be viewed as a liberation of the classical isometry group of the p-dimensional torus. 相似文献
5.
In this paper, we study global positive C4 solutions of the geometrically interesting equation: Δ2u+u−q=0 with q>0 in R3. We will establish several existence and non-existence theorems, including the classification result for q=7 with exactly linear growth condition. 相似文献
6.
Suemi Rodríguez-Rorno 《代数通讯》2013,41(9):4307-4325
Following the method already developed for studying the actions of GLq (2,C) on the Clifford algebra C(l,3) and its quantum invariants [1], we study the action on C(l, 3) of the quantum GL 2 constructed by Dipper and Donkin [2]. We are able of proving that there exits only two non-equivalent cases of actions with nontrivial “perturbation” [1]. The spaces of invariants are trivial in both cases. We also prove that each irreducible finite dimensional algebra representation of the quantum GL 2 qm ≠1, is one dimensional. By studying the cases with zero “perturbation” we find that the cases with nonzero “perturbation” are the only ones with maximal possible dimension for the operator algebra ?. 相似文献
7.
BIPUL SAURABH 《Proceedings Mathematical Sciences》2017,127(1):133-164
For the quantum symplectic group SP q (2n), we describe the C ?-algebra of continuous functions on the quotient space S P q (2n)/S P q (2n?2) as an universal C ?-algebra given by a finite set of generators and relations. The proof involves a careful analysis of the relations, and use of the branching rules for representations of the symplectic group due to Zhelobenko. We then exhibit a set of generators of the K-groups of this C ?-algebra in terms of generators of the C ?-algebra. 相似文献
8.
9.
Melvyn B. Nathanson 《Journal of Number Theory》2003,103(2):214-233
For the quantum integer [n]q=1+q+q2+?+qn−1 there is a natural polynomial multiplication such that [m]q⊗q[n]q=[mn]q. This multiplication leads to the functional equation fm(q)fn(qm)=fmn(q), defined on a given sequence of polynomials. This paper contains various results concerning the construction and classification of polynomial sequences that satisfy the functional equation, as well open problems that arise from the functional equation. 相似文献
10.
We prove several new results on the absolutely continuous spectra of perturbed one-dimensional Stark operators. First, we find new classes of perturbations, characterized mainly by smoothness conditions, which preserve purely absolutely continuous spectrum. Then we establish stability of the absolutely continuous spectrum in more general situations, where imbedded singular spectrum may occur. We present two kinds of optimal conditions for the stability of absolutely continuous spectrum: decay and smoothness. In the decay direction, we show that a sufficient (in the power scale) condition is |q(x)|≤C(1+|x|)?1/4?ε; in the smoothness direction, a sufficient condition in Hölder classes isq∈C1/2+ε(R). On the other hand, we show that there exist potentials which both satisfy |q(x)|≤C(1+|x|)?1/4 and belong toC1/2(R) for which the spectrum becomes purely singular on the whole real axis, so that the above results are optimal within the scales considered. 相似文献
11.
Ernst-Ulrich Gekeler 《manuscripta mathematica》2014,144(3-4):401-420
We study n-point configurations in \({\mathbb{P}^1(\mathbb{F}_q)}\) modulo projective equivalence. For n = 4 and 5, a complete classification is given, along with the numbers of such configurations with a given symmetry group. Using Polya’s coloring theorem, we investigate the behavior of the numbers C(n, q) of classes of n-configurations resp. C spec(n, q) of classes with nontrivial symmetry group. Both are described by rational polynomials in q which depend on q modulo \({\lambda(n) = {\rm lcm} \{m \in \mathbb{N} | m \leq n\}}\) . 相似文献
12.
We consider a second-order differential equation −y″ + q(x)y(x) = λy(x) with complex-valued potential q and eigenvalue parameter λ ∈ ℂ. In PT quantum mechanics the potential q is given by q(x) = −(ix)N+2 on a contour Γ ⊂ ℂ. Via a parametrization we obtain two differential equations on [0, ∞) and (−∞, 0]. We give a limit-point/limit-circle classification of this problem via WKB-analysis. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
Let q be an odd prime power, and suppose q?1 (mod8), Let C(q) and C(q)1 be the two extended binary quadratic residue codes (QR codes) of length q+1, and let . We establish a square root bound on the minimum weight in T(q). Since the same type of bound applies to C(q) and C(q)1, this is a good method of combining codes. 相似文献
14.
We study the approximation of functions from anisotropic Sobolev classes B(Wrp([0,1]d)) and Hölder-Nikolskii classes B(Hrp([0,1]d)) in the Lq([0,1]d) norm with q ≤ p in the quantum model of computation. We determine the quantum query complexity of this problem up to logarithmic factors. It shows that the quantum algorithms are significantly better than the classical deterministic or randomized algorithms. 相似文献
15.
Xuejun Zhang 《Journal of Mathematical Analysis and Applications》2003,285(2):376-386
In the paper, we will discuss the pointwise multipliers from Dirichlet type space Dp to Bloch type space βq on the unit ball of Cn. The multiplier spaces M(Dp,βq) are fully characterized for all p, q. 相似文献
16.
《Journal of Computational and Applied Mathematics》1987,18(2):163-174
We examine the problem ϵ(p(x)u′) + (q(x)u)′ − r(x)u = f(x) for 0 < x < 1, p>0, q>0, r ⩾ 0; p, q, r and f in C2[0, 1], ϵ in (0, 1], u(0) and u(1) given. Existence of a unique solution u and bounds on u and its derivatives are obtained. Using finite elements on an equidistant mesh of width h we generate a tridiagonal difference scheme which is shown to be uniformly second order accurate for this problem (i.e., the nodal errors are bounded by Ch2, where C is independent of h and ϵ). With a natural choice of trial functions, uniform first order accuracy is obtained in the L∞(0, 1) norm. Using trial functions which interpolate linearly between the nodal values generated by the difference scheme gives uniform first order accuracy in the L1(0, 1) norm. 相似文献
17.
A. I. Mudrov 《Theoretical and Mathematical Physics》2017,192(2):1205-1217
Let g′ ? g be a pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces C N?2 ? C N and U q (g′) ? U q (g) be a pair of quantum groups with a triangular decomposition U q (g) = U q (g-)U q (g+)U q (h). Let Z q (g, g′) be the corresponding step algebra. We assume that its generators are rational trigonometric functions h ? → U q (g±). We describe their regularization such that the resulting generators do not vanish for any choice of the weight. 相似文献
18.
In this paper we give a method for obtaining the adjacency matrix of a simple polarity graph G q from a projective plane PG(2, q), where q is a prime power. Denote by ex(n; C 4) the maximum number of edges of a graph on n vertices and free of squares C 4. We use the constructed graphs G q to obtain lower bounds on the extremal function ex(n; C 4), for some n < q 2 + q + 1. In particular, we construct a C 4-free graph on ${n=q^2 -\sqrt{q}}$ vertices and ${\frac{1}{2} q(q^2-1)-\frac{1}{2}\sqrt{q} (q-1) }$ edges, for a square prime power q. 相似文献
19.
Let q be an integer ≥2 and Ω a suitable subset of {0,…,q ? 1}2; (q; Ω) denotes the set of natural integers, the pairs of successive q-adic digits of which are in Ω. If P is an irrational polynomial, the sequence (P(n): n ∈ (q; Ω)) is uniformly distributed modulo one. 相似文献
20.
Olivier Gabriel 《Annales Henri Poincare》2014,15(5):1013-1036
Given an action of a Compact Quantum Group (CQG) on a finite dimensional Hilbert space, we can construct an action on the associated Cuntz algebra. We study the fixed point algebra of this action, using Kirchberg classification results. Under certain conditions, we prove that the fixed point algebra is purely infinite and simple. We further identify it as a C *-algebra, compute its K-theory and prove a “stability property”: the fixed points only depend on the CQG via its fusion rules. We apply the theory to SU q (N) and illustrate by explicit computations for SU q (2) and SU q (3). This construction provides examples of free actions of CQG (or “principal noncommutative bundles”). 相似文献