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# A Note on Amenability of Locally Compact Quantum Groups

Published:2012-11-13

• 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
 MSC Classifications: 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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