Quantum real projective space, disc and sphere

Piotr M. Hajac, Rainer Matthes, and Wojciech Szymanski

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Submission date: 14. Oct. 2000
Pages: 24
published in: Algebras and representation theory, 6 (2003) 2, p. 169-192 
DOI number (of the published article): 10.1023/A:1023288309786
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Abstract:
We define the C^*-algebra of quantum real projective space RP_q², classify its irreducible representations and compute its K-theory. We also show that the q-disc of Klimek-Lesniewski can be obtained as a non-Galois Z₂-quotient of the equator Podles quantum sphere. On the way, we provide the Cartesian coordinates for all Podles 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.