The Compact Quantum Group U q (2) ( II)

Xiao Zhang
July 2006
Acta Mathematica Sinica;Jul2006, Vol. 22 Issue 4, p1221
Academic Journal
In this paper, we first prove that the θ-deformation U θ (2) of U(2) constructed by Connes and Violette is our special case of the quantum group U q (2) constructed in our previous paper. Then we will show that the set of traces on the C*–algebra U θ , θ irrational, is determined by the set of the traces on a subalgebra of U θ .


Related Articles

  • Some Counterexamples in the Theory of Quantum Isometry Groups. Bhowmick, Jyotishman; Goswami, Debashish // Letters in Mathematical Physics;Sep2010, Vol. 93 Issue 3, p279 

    By considering spectral triples on $${S^{2}_{\mu, c}\,\, (c >0 )}$$ constructed by Chakraborty and Pal (Commun Math Phys 240(3):447–456, 2000), we show that in general the quantum group of volume and orientation preserving isometries (in the sense of Bhowmick and Goswami in J Funct Anal...

  • WAKIMOTO REALIZATION OF THE ELLIPTIC QUANTUM GROUP $U_{q,p}(\widehat{{\rm sl}_N})$. KOJIMA, TAKEO // International Journal of Modern Physics A: Particles & Fields; G;12/10/2009, Vol. 24 Issue 30, p5561 

    We construct a free field realization of the elliptic quantum algebra $U_{q,p}(\widehat{{\rm sl}_N})$ for arbitrary level k ≠ 0, -N. We study Drinfeld current and the screening current associated with $U_{q,p}(\widehat{{\rm sl}_N})$ for arbitrary level k. In the limit p → 0 this...

  • The Inhomogeneous Quantum Invariance Group of The Two Parameter Deformed Boson Algebra. Alim, Huseyin; Altintas, Azmi Ali; Arik, Metin; Arikan, Ali Serdar // International Journal of Theoretical Physics;Mar2010, Vol. 49 Issue 3, p633 

    We consider two parameter deformed boson algebra and investigate the inhomogeneous invariance quantum group of this system. We find the R-matrix which collects all information about the non-commuting structure of the quantum group. We extend our study to the d-dimensional case.

  • A locally compact quantum group of triangular matrices. Fima, P.; Vainerman, L. // Ukrainian Mathematical Journal;Apr2008, Vol. 60 Issue 4, p648 

    We construct a one-parameter deformation of the group of 2 � 2 upper triangular matrices with determinant 1 using the twisting construction. An interesting feature of this new example of a locally compact quantum group is that the Haar measure is deformed in a nontrivial way. We also give a...

  • On Generic Extensions of Representations of a Dynkin Quiver of Type D. Deng, Xiao; Chen, Jiang // Acta Mathematica Sinica;Jun2005, Vol. 21 Issue 3, p613 

    The notion of generic extensions of representations of a Dynkin quiver plays a big role in the study of the structure of the corresponding quantum group. In this paper, we describe the generic extensions of a simple representation by any representation and that of any representation by a simple...

  • Non-Semi-Regular Quantum Groups Coming from Number Theory. Baaj, Saad; Skandalis, Georges; Vaes, Stefaan // Communications in Mathematical Physics;Apr2003, Vol. 235 Issue 1, p139 

    : In this paper, we study C*-algebraic quantum groups obtained through the bicrossed product construction. Examples using groups of adeles are given and they provide the first examples of locally compact quantum groups which are not semi-regular: the crossed product of the quantum group acting...

  • Quantum Groups and Double Quiver Algebras. Huang, Hua-Lin; Yang, Shilin // Letters in Mathematical Physics;Jan2005, Vol. 71 Issue 1, p49 

    For a finite dimensional semisimple Lie algebraand a rootqof unity in a fieldk, we associate to these data a double quiver. It is shown that a restricted version of the quantized enveloping algebrasis a quotient of the double quiver algebra.

  • A Problem of Classification of Quantum Groups. Fronsdal, C. // Physics of Atomic Nuclei;Oct2005, Vol. 68 Issue 10, p1670 

    An attempt to formulate a precise program of classification of a large family of quantum groups is presented. This family includes the familiar quantum groups and quantum supergroups, but much more, all unified in a very simple structure. The emphasis is on the logic of the classification...

  • Semilattice graded weak Hopf algebra and its related quantum G-double. Fang Li; Haijun Cao // Journal of Mathematical Physics;Aug2005, Vol. 46 Issue 8, p083519 

    The major purpose of this paper is to construct a weak Hopf algebra with grading from a family of Hopf algebras, and then to gain a related quantum G-double with regular R-matrix. First, over a field k, we introduce a so-called semilattice graded weak Hopf algebra H=+α∈YHα. Then the...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics