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Quantum Bohr compactification. (English) Zbl 1099.46048
Summary: We introduce a non-commutative analog of the Bohr compactification. Starting from a general quantum group \(G\), we define a compact quantum group \(\mathfrak{b}G\), which has a universal property such as the universal property of the classical Bohr compactification for topological groups. We study the object \(\mathfrak{b}G\) in the special cases when \(G\) is a classical locally compact group, the dual of a classical group, a discrete or compact quantum group, and a quantum group arising from a manageable multiplicative unitary. We also use our construction to give new examples of compact quantum groups.

MSC:
46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory
58B32 Geometry of quantum groups
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
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