Algebras and Representation Theory

, Volume 6, Issue 2, pp 169–192

Quantum Real Projective Space, Disc and Spheres


  • Piotr M. Hajac
    • Polish Academy of SciencesMathematical Institute
    • Department of Mathematical Methods in PhysicsWarsaw University
  • Rainer Matthes
    • Max Planck Institute for Mathematics in the Sciences
    • Institute of Theoretical PhysicsLeipzig University
  • Wojciech Szymański
    • School of Mathematical and Physical SciencesUniversity of Newcastle

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


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.


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© Kluwer Academic Publishers 2003