Quantum Real Projective Space, Disc and Sphere
Piotr M. Hajac, Rainer Matthes, Wojciech Szymanski

TL;DR
This paper introduces the $C^*$-algebra of quantum real projective space, classifies its irreducible representations, computes its $K$-theory, and relates the $q$-disc to the Podleś quantum sphere, expanding the understanding of quantum geometric structures.
Contribution
It defines the $C^*$-algebra of quantum real projective space, classifies its irreducible representations, and establishes a connection between the $q$-disc and Podleś quantum sphere.
Findings
Classified irreducible representations of $ ext{C}^*( ext{RP}_q^2)$
Computed the $K$-theory of quantum real projective space
Related the $q$-disc to the Podleś quantum sphere as a non-Galois $ ext{Z}_2$-quotient
Abstract
We define the -algebra of quantum real projective space , classify its irreducible representations and compute its -theory. We also show that the -disc of Klimek-Lesniewski can be obtained as a non-Galois -quotient of the equator Podle\'s quantum sphere. On the way, we provide the Cartesian coordinates for all Podle\'s quantum spheres and determine an explicit form of isomorphisms between the -algebras of the equilateral spheres and the -algebra of the equator one.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Operator Algebra Research
