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A Note on Amenability of Locally Compact Quantum Groups

  Published:2012-11-13
 Printed: Jun 2014
  • Piotr M. Sołtan,
    Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Poland
  • Ami Viselter,
    Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1
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Abstract

In this short note we introduce a notion called ``quantum injectivity'' of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. Particularly, this provides a new characterization of amenability of locally compact groups.
Keywords: amenability, conditional expectation, injectivity, locally compact quantum group, quantum injectivity amenability, conditional expectation, injectivity, locally compact quantum group, quantum injectivity
MSC Classifications: 20G42, 22D25, 46L89 show english descriptions Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
$C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]
Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
20G42 - Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
22D25 - $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]
46L89 - Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
 

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