Weak Amenability of Locally Compact Quantum Groups and Approximation Properties of Extended Quantum SU(1, 1)

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Induced corepresentations of locally compact quantum groups

Consider a closed subgroup H of a locally compact group G together with a strongly continuous unitary representation u of H on a Hilbert space K. The construction of the induced representation uses these three ingredients to supply a new strongly continuous unitary representation ρ of the larger group G on a new Hilbert space K. Induced group representations for finite groups where first introd...

Asymptotic invariance properties for locally compact quantum groups

Let G be a locally compact group. Then G is known to be amenable if and only if it satisfies property (P1), i.e., there is a net (mα)α of non-negative norm one functions in L(G) such that limα supx∈K ‖Lx−1mα −mα‖ = 0 for each compact subset K ⊂ G (Lx−1mα stands for the left translate of mα by x ). We give a formulation of propety (P1) that extends naturally to locally compact quantum groups in ...

Uniform continuity over locally compact quantum groups

We define, for a locally compact quantum group G in the sense of Kustermans– Vaes, the space of LUC (G) of left uniformly continuous elements in L∞(G). This definition covers both the usual left uniformly continuous functions on a locally compact group and Granirer’s uniformly continuous functionals on the Fourier algebra. We show that LUC (G) is an operator system containing the C∗-algebra C0(...

Quasi-Discrete Locally Compact Quantum Groups

Let A be a C *-algebra. Let A ⊗ A be the minimal C *-tensor product of A with itself and let M (A ⊗ A) be the multiplier algebra of A ⊗ A. A comultiplication on A is a non-degenerate *-homomorphism ∆ : A → M (A ⊗ A) satisfying the coassociativity law (∆ ⊗ ι)∆ = (ι ⊗ ∆)∆ where ι is the identity map and where ∆ ⊗ ι and ι ⊗ ∆ are the unique extensions to M (A ⊗ A) of the obvious maps on A ⊗ A. We ...