Quantum Real Projective Space, Disc and Spheres
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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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