Quantum Real Projective Space, Disc and Sphere

Abstract

We define the C *-algebra of quantum real projective space R P q 2, 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 Z 2-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.