Locally compact quantum groups

By J. Kustermans, S. Vaes. 2000

219 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b76b438d6e432d1560a7843245d238f2950b0b9d

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In Statistical and Nonlinear Physics

Citations in the corpus

Measurable Schur Multipliers and Completely Bounded Multipliers of the Fourier Algebras (2002, methodology): “ngst others. It thus gives a starting point for obtaining representations of completely multipliers ofKac algebras, after [28] orof multipliers of locally compact quantum groups after Vaes et al (see [44]). To support our approach, in Section 3 we describe the space of measurable Schur multipliers, ”
Quantum automorphism groups of vertex-transitive graphs of order ≤ 11 (2006, background): “ulae are made into precise statements in the ﬁrst section of Woronowicz’ seminal paper [19]. They are pieces of Pontryagin duality for locally compact quantum groups, whose latest version is given in [11]. The compact quantum group morphisms are deﬁned in the usual manner: if A = C(G) and B = C(H) a”
Towards a full solution of the large N double-scaled SYK model (2018, methodology): “[42] A more detailed and careful approach goes via so called von Neumann algebraic quantum groups [44, 45], see in particular [50, 71] where a properly defined non-compact quantum group SUext q (1, 1) [43] is constructed.”
Locally compact quantum groups (2017, methodology): “Then there are the original papers [22] and [23] of which [22] contains all the essential proofs.”
Locally Compact Quantum Groups. A von Neumann Algebra Approach (2006, methodology): “e original C-algebra, we need the extra density conditions as they are found in the original definition of a locally compact quantum group in the C-algebra setting (as given by Kustermans and Vaes in [7]). We recall the definition here. Denition A.10. Let Abe a C-algebra and a comultiplication on A(”
Extensions of locally compact quantum groups and the bicrossed product construction (2001, methodology): “In view of [26], Proposition 8.”
Strictly Outer Actions of Groups and Quantum Groups (2002, background): “ we get a strictly positive, self-adjoint operator ρaﬃliated with Msuch that ∆(ρ it) = ρit⊗ρitfor all t∈ R and τ t= Adρ . Because ∆(ρ) = ρ⊗ ρ, it follows with the same proof as in Proposition 7.10 of [22] that ρis aﬃliated (in the C ∗-algebraic sense) with the C -algebra of (M,∆). This C -algebra is”
From multiplicative unitaries to quantum groups II (2007, background): “The importance of manageability was emphasized with appearance the famous paper [8] in which Kustermans and Vaes gave a very satisfactory definition of a locally compact quantum group.”