# Quantum random walk for U[sub q](su)(2)) and a new example of quantum noise

## Related Articles

- A noncommutative Hopf structure on C[sup infinity][SL(2,)] as a quantum Lorentz group. Martin, Christiane; Zouagui, Mohamed // Journal of Mathematical Physics;Jul96, Vol. 37 Issue 7, p3611
Examines a classical Frechet Hopf algebra containing the quantum deformation of the enveloping Lorentz algebra. Isomorphic characteristics to quasitriangular twisted topological sensor product Hopf algebra; Topological dual space.

- Sub-Hopf-algebra-induced twists of quantum enveloping algebras. Engeldinger, Ralf A.; Kempf, Achim // Journal of Mathematical Physics;Apr94, Vol. 35 Issue 4, p1931
It is shown that a quasitriangular Hopf algebra can be twisted by the universal R-matrix of any quasitriangular sub-Hopf algebra and examples are given of R-matrices of quantum groups obtained this way.

- Mapping Class Group Representations and Generalized Verlinde Formula. Bántay, Peter; Vecsernyés, Peter // International Journal of Modern Physics A: Particles & Fields; G;4/10/99, Vol. 14 Issue 9, p1325
Unitary representations of centrally extended mapping class groups &Mtilde;[sub g,1], g â‰¥ 1 are given in terms of a rational Hopf algebra H, and a related generalization of the Verlinde formula is presented. Formulae expressing the traces of mapping class group elements in terms of the...

- On the addition of quantum matrices. Majid, S. // Journal of Mathematical Physics;May94, Vol. 35 Issue 5, p2617
An addition law is introduced for the usual quantum matrices A(R) by means of a coaddition Î”t=tâŠ—l+lâŠ—t. It supplements the usual comultiplication Î”t=tâŠ—t. and together they obey a codistributivity condition. The coaddition does not form a usual Hopf algebra but a braided...

- The twisted Heisenberg algebra U[sub h, w](H(4)). Abdesselam, Boucif // Journal of Mathematical Physics;Dec97, Vol. 38 Issue 12, p6045
Analyzes parametric deformations of the enveloping Heisenberg algebra that appears as a combination of the standard and nonstandard quantization. Mathematical proof of its existence as a Ribbon Hopf algebra; Universal matrices of the Heiseberg algebra; Solution of the Braid group; Parameters of...

- Quantum deformations of nonsemisimple algebras: The example of D=4 inhomogeneous rotations. Lukierski, Jerzy; Ruegg, Henri; Nowicki, Anatol // Journal of Mathematical Physics;May94, Vol. 35 Issue 5, p2607
A general class of deformations of the complexified D=4 PoincarÃ© algebra O(3,1;C)...T[sub 4](C) is considered with a classical (undeformed) subalgebra 0(3;C)...T[sub 4](C) and deformed relations preserving the O(3;C) tensor structure. We distinguish the class of quantum...

- A new quasitriangular Hopf algebra as the nontrivial quantum double of a simplest C algebra and its universal R matrix for Yangâ€“Baxter equation. Sun, Chang-Pu; Liu, Xu-Feng; Ge, Mo-Lin // Journal of Mathematical Physics;Mar1993, Vol. 34 Issue 3, p1218
Endowing a simple C algebra generated by two commuting elements and a unit with a noncocommutative Hopf algebra structure, a new quantum double and the corresponding universal R matrix for the Yangâ€“Baxter equation is constructed. The finite-dimensional representations of the quantum...

- The realizations of quantum groups of An-1 and Cn types in q-deformed oscillator systems at classical and quantum levels. Chang, Zhe; Wang, Jian-Xiong; Yan, Hong // Journal of Mathematical Physics;Dec91, Vol. 32 Issue 12, p3241
In the classical q-deformed oscillators system, the Poisson bracket realizations of the quantum enveloping algebras of An-1 and Cn types are given in the symplectic space (V,Î©) (without deformation). When the oscillators system is canonically quantized, the Lie bracket realizations of the...

- Differential Hopf algebra structure of the quantum standard complex. Drabant, Bernhard // Journal of Mathematical Physics;May97, Vol. 38 Issue 5, p2652
Studies the quantum standard complex (K(q,g),d) of the quantum enveloping algebra for Lie algebras. Quantum version of the standard Koszul complex associated to a Lie algebra; Differential Hopf algebra structure of the complex obtained from the theory of braided monoidal categories.