Podleś Spheres for the Braided Quantum SU(2)

2019/09/11 by Piotr M. Sołtan, Sołtan, Piotr M.
Mathematics · #17B37 #46L89 (secondary) #58B32 (primary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1909.05000

openalex publication_date 2019/09/11 · openalex created_date 2019/09/19 · openalex updated_date 2026/07/28

Abstract

Starting with the braided quantum group SU_q(2) for a complex deformation parameter q we perform the construction of the quotient SU_q(2)/\mathbbT which serves as a model of a quantum sphere. Then we follow the reasoning of Podleś who for real q classified quantum spaces with the action of SU_q(2) with appropriate spectral properties. These properties can also be expressed in the context of the braided quantum SU_q(2) (with complex q) and we find that they lead to precisely the same family of quantum spaces as found by Podleś for the real parameter |q|.

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