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A locally compact quantum group (in the sense of Vaes-Kustermans) consists of the data $(M, \Delta, \varphi, \psi)$ with $M$ a von Neumann algebra, $\Delta: M \to M \overline{\otimes} M$ a normal ...

Let us consider the enveloping algebra $\mathcal{U}(\mathfrak{g})$ of some Lie algebra $\mathfrak{g}$. Under what assumptions about $\mathfrak{g}$, does the enveloping algebra generate a locally ...

This question was originally posted to MathStackExchange. Let $\mathbb{G}$ be a locally compact quantum group and let $W$ and $V$ be the left and right fundamental unitaries, i.e., they implement the ...

I have read some articles on locally compact quantum groups and the Fourier Transform on them. I wonder why we define the Fourier transform as an operator valued functions from $L^1(\mathbb{G})$ to $L^...

Let $\mathcal{A}$ be the category of $C^*$ algebras. For a group $G$ let $\tilde{G}$ be the space of all conjugacy classes of $G$. What is a precise description of a maximal ,or in some sense ...

Consider a (von Neumann algebraic) locally compact quantum group $(M, \Delta, \phi, \psi)$ where the von Neumann algebra $M$ is realized as operators on the Hilbert space $H$. There is a ...