• Debashish Goswami
  • Jyotishman Bhowmick
Part of the Infosys Science Foundation Series book series (ISFS)


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.


Hopf Algebra Quantum Group Compact Quantum Group Hilbert Module Weak Operator Topology 
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Copyright information

© Springer (India) Pvt. Ltd 2016

Authors and Affiliations

  1. 1.Statistics and Mathematics UnitIndian Statistical InstituteKolkataIndia

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