Annals of Functional Analysis

Isomorphisms of discrete multiplier Hopf $C^*$-bialgebras: the nontracial case

Dan Z. Kucerovsky

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We construct Hopf algebra isomorphisms of discrete (multiplier) Hopf $C^*$-bialgebras from $K$-theoretical data, without assuming that the Haar weight is tracial.

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Ann. Funct. Anal., Volume 6, Number 3 (2015), 166-175.

First available in Project Euclid: 17 April 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
Secondary: 16W30 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]

Hopf algebra $C^*$-algebra $K$-theory fusion ring


Kucerovsky, Dan Z. Isomorphisms of discrete multiplier Hopf $C^*$-bialgebras: the nontracial case. Ann. Funct. Anal. 6 (2015), no. 3, 166--175. doi:10.15352/afa/06-3-14.

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  • E. Abe, Hopf Algebras, Cambridge University Press, London, 1980.
  • S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de $C^*$-algèbres, Ann. Sci. École Norm. Sup. 4 (1993), 425–488.
  • T. Banica, Fusion Rules for Representations of Compact Quantum Groups, Expo. Math., 17 (1999), 313–338.
  • B. Blackadar, Operator algebras: Theory of $C^{*}$-algebras and von Neumann algebras, Springer-Verlag, Berlin, 2006.
  • M. Daws and H. Le Pham, Isometries between quantum convolution algebras, Q. J. Math. 64 (2013), 373–396.
  • S. Dăscălescu, C. Năstăsescu, and Ş. Raianu, Hopf Algebras, Marcel Dekker Inc., New York, 2001.
  • P. Fima, Kazhdan's property T for discrete quantum groups, Internat. J. Math. 21 (2010), no. 1, 47–65.
  • B.-J. Kahng, Fourier transform on locally compact quantum groups, J. Operator Theory 64 no. 1 (2010), 69–87.
  • D. Kučerovský, On convolution products and automorphisms in Hopf $C^*$-algebras, Positivity 18 (2014), no. 3, 595–601.
  • D. Kučerovský, An abstract classification of finite-dimensional Hopf $C^*$-algebras, Comptes Rendus Math. (Canada), 36 (4) 2014, 97–105.
  • D. Kučerovský, Isomorphisms and automorphisms of discrete multiplier Hopf $C^*$-algebras, Positivity 19 (2015), no. 1, 161–175.
  • J. Kustermans and S. Vaes, Locally compact quantum groups, Ann. Scient. École Norm. Sup., (4) 33 (2000), no. 6, 837–934.
  • E. Størmer, On the Jordan structure of $C^*$-algebras, Trans. Amer. Math. Soc. 120 (1965) 438–447.
  • T. Timmermann, An Invitation to Quantum Groups and Duality, EMS Textbooks in Mathematics, EMS Publishing House, Zürich, Switzerland, 2008.
  • A. Van Daele, Multiplier Hopf algebras, Trans. Amer. Math. Soc. 342 (1994), 917–932.
  • A. Van Daele, Discrete quantum groups, J. Algebra 180 (1996), 431–444.
  • A. Van Daele, An Algebraic Framework for Group Duality, Advances in Math. 140 (1998), 323–366.
  • A. Van Daele, Locally compact quantum groups: the von Neumann algebra versus the $C^*$-algebra approach, J Bull. Kerala Math. Assoc. (2007), 153–177.