Quantum real projective space, disc and sphere
Piotr M. Hajac, Rainer Matthes,and Wojciech Szymanski
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Submission date: 14. Oct. 2000
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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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-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.