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Preliminaries

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Quantum Isometry Groups

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Abstract

In this chapter, we discuss the basic concepts and results needed in the later chapters of the book. Beginning with a glimpse of operator algebras and Hilbert modules, free product and tensor products of \( C^* \) algebras and some examples, we proceed to the generalities on quantum groups including the basics of Hopf algebras and compact quantum groups as well as some concrete examples such as \(U_{\mu } (2), SU_{\mu } (2), \mathcal{U}_{\mu } (su(2)) \) and \( SO_{\mu } ( 3 ). \) We also introduce the notion of a \(C^*\) coaction of a compact quantum group on a \(C^*\) algebra and give an account of Shuzhou Wang’s work in [35] and [42]. We discuss the example of the action of \( SO_{\mu } ( 3 ) \) on Podles’ spheres in details.

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Authors and Affiliations

  1. Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, India

    Debashish Goswami & Jyotishman Bhowmick

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  1. Debashish Goswami
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  2. Jyotishman Bhowmick
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Correspondence to Debashish Goswami .

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Goswami, D., Bhowmick, J. (2016). Preliminaries. In: Quantum Isometry Groups. Infosys Science Foundation Series(). Springer, New Delhi. https://doi.org/10.1007/978-81-322-3667-2_1

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