Compact quantum subgroups and left invariant C*-subalgebras of locally compact quantum groups

Details Compact quantum subgroups and left invariant C*-subalgebras of locally compact quantum groups Compact quantum subgroups and left invariant C*-subalgebras of locally compact quantum groups

2010-04-23

arxiv.org/abs/1004.4161v3

Pekka Salmi, Compact quantum subgroups and left invariant C*-subalgebras of locally compact quantum groups, Journal of Functio

Mathematics

Operator Algebras

21 pages. Final version. Minor edits to version 2

Scientific paper

We show that there is a one-to-one correspondence between compact quantum subgroups of a co-amenable locally compact quantum group $\mathbb{G}$ and certain left invariant C*-subalgebras of $C_0(\mathbb{G})$. We also prove that every compact quantum subgroup of a co-amenable quantum group is co-amenable. Moreover, there is a one-to-one correspondence between open subgroups of an amenable locally compact group $G$ and non-zero, invariant C*-subalgebras of the group C*-algebra $C^*(G)$.

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