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On Positive Definiteness over Locally Compact Quantum Groups

  Published:2016-03-28
 Printed: Oct 2016
  • Volker Runde,
    Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
  • Ami Viselter,
    Department of Mathematics, University of Haifa, 31905 Haifa, Israel
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Abstract

The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various well-known results about positive-definite functions over groups to the quantum framework. Among these are theorems on "square roots" of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.
Keywords: bicrossed product, locally compact quantum group, non-commutative $L^p$-space, positive-definite function, positive-definite measure, separation property bicrossed product, locally compact quantum group, non-commutative $L^p$-space, positive-definite function, positive-definite measure, separation property
MSC Classifications: 20G42, 22D25, 43A35, 46L51, 46L52, 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]
Positive definite functions on groups, semigroups, etc.
Noncommutative measure and integration
Noncommutative function spaces
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]
43A35 - Positive definite functions on groups, semigroups, etc.
46L51 - Noncommutative measure and integration
46L52 - Noncommutative function spaces
46L89 - Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
 

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