Algebras and Representation Theory

, Volume 6, Issue 2, pp 169–192

Quantum Real Projective Space, Disc and Spheres

  • Piotr M. Hajac
  • Rainer Matthes
  • Wojciech Szymański
Article

DOI: 10.1023/A:1023288309786

Cite this article as:
Hajac, P.M., Matthes, R. & Szymański, W. Algebras and Representation Theory (2003) 6: 169. doi:10.1023/A:1023288309786

Abstract

We define the C*-algebra of quantum real projective space RPq2, classify its irreducible representations, and compute its K-theory. We also show that the q-disc of Klimek and Lesniewski can be obtained as a non-Galois Z2-quotient of the equator Podleś quantum sphere. On the way, we provide the Cartesian coordinates for all Podleś quantum spheres and determine an explicit form of isomorphisms between the C*-algebras of the equilateral spheres and the C*-algebra of the equator one.

C*-representationsK-theory

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Piotr M. Hajac
    • 1
    • 2
  • Rainer Matthes
    • 3
    • 4
  • Wojciech Szymański
    • 5
  1. 1.Polish Academy of SciencesMathematical InstituteWarsawPoland
  2. 2.Department of Mathematical Methods in PhysicsWarsaw UniversityWarsawPoland
  3. 3.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  4. 4.Institute of Theoretical PhysicsLeipzig UniversityLeipzigGermany
  5. 5.School of Mathematical and Physical SciencesUniversity of NewcastleCallaghanAustralia