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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
##### Keywords:
Bohr compactification; quantum group
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