Piotr M. Sołtan,
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.
amenability, conditional expectation, injectivity, locally compact quantum group, quantum injectivity
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]