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

Abstract

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 $C^{\ast }(G)$.

21 pages. Final version. Minor edits to version 2

References in corpus (1)

• Locally Compact Quantum Groups. A von Neumann Algebra Approach

Cited by in corpus (1)

• Noncommutative homogeneous spaces: the matrix case