Related papers: On Ideals of $L^1$-algebras of Compact Quantum Gro…

We introduce an appropriate notion of inner amenability for locally compact quantum groups, study its basic properties, related notions, and examples arising from the bicrossed product construction. We relate these notions to homological…

We study relative amenability and amenability of a right coideal $\widetilde{N}_P\subseteq \ell^\infty(\mathbb{G})$ of a discrete quantum group in terms of its group-like projection $P$. We establish a notion of a $P$-left invariant state…

We classify the weak*-closed maximal left ideals of the measure algebra $M(G)$ for certain Hermitian locally compact groups $G$ in terms of the irreducible representations of $G$ and their asymptotic properties. In particular, we obtain a…

For a locally compact quantum group $\mathbb{G}$, a (left) coideal is a (left) $\mathbb{G}$-invariant von Neumann subalgebra of $L^\infty(\mathbb{G})$. We introduce and analyze various generalizations of amenability and coamenability to…

Building on our previous work, we study the non-relative homology of quantum group convolution algebras. Our main result establishes the equivalence of amenability of a locally compact quantum group $\mathbb{G}$ and 1-injectivity of…

Let $\mathbb{G}$ be a locally compact quantum group. We give a 1-1 correspondence between group-like projections in $L^\infty(\mathbb{G})$ preserved by the scaling group and idempotent states on the dual quantum group…

Given a locally compact quantum group $\mathbb G$, we define and study representations and C$^\ast$-completions of the convolution algebra $L_1(\mathbb G)$ associated with various linear subspaces of the multiplier algebra $C_b(\mathbb G)$.…

We determine the space of primary ideals in the group algebra $L^1(G)$ of a connected nilpotent Lie group by identifying for every $\pi\in\hat G $ the family ${\mathcal I}^\pi $ of primary ideals with hull $\{\pi\}$ with the family of…

Let $G$ be a right-angled Artin group with $|\mathrm{Out}(G)|<+\infty$. We prove that if a countable group $H$ with bounded torsion is measure equivalent to $G$, with an $L^1$-integrable measure equivalence cocycle towards $G$, then $H$ is…

We discuss necessary conditions for a compact quantum group to act on the algebra of noncommutative $n$-torus $\mathbb{T}_\theta^n$ in a filtration preserving way in the sense of Banica and Skalski. As a result, we construct a family of…

The semidirect product $\mathbb{G}=\mathbb{L}\rtimes \mathbb{K}$ attached to a compact-group action on a connected, simply-connected solvable Lie group has a dense set of compact elements precisely when the $s\in \mathbb{K}$ operating on…

We prove that any meager quasi-analytic subgroup of a topological group $G$ belongs to every $\sigma$-ideal $\mathcal I$ on $G$ possessing the closed $\pm n$-Steinhaus property for some $n\in\mathbb N$. An ideal $\mathcal I$ on a…

We prove that if $G$ is a noncompact connected real reductive linear Lie group, then any discrete subgroup of $G$ acting properly discontinuously and cocompactly on some homogeneous space $G/H$ of $G$ is quasi-isometrically embedded and…

For any topological group $G$ the dual object $\hat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat G$ is discrete, and we investigate…

We study the dual relationship between quantum group convolution maps $L^1(\mathbb{G})\rightarrow L^{\infty}(\mathbb{G})$ and completely bounded multipliers of $\widehat{\mathbb{G}}$. For a large class of locally compact quantum groups…

We prove a number of results having to do with equipping type-I $\mathrm{C}^*$-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the…

We show that the convolution algebra of smooth, compactly-supported functions on a Lie groupoid is H-unital in the sense of Wodzicki. We also prove H-unitality of infinite order vanishing ideals associated to invariant, closed subsets of…

We introduce notions of finite presentation and co-exactness which serve as qualitative and quantitative analogues of finite-dimensionality for operator modules over completely contractive Banach algebras. With these notions we begin the…

We show that for a Hecke pair $(G, \Gamma)$ the $C^*$-completions $C^*(L^1(G, \Gamma))$ and $pC^*(\bar{G})p$ of its Hecke algebra coincide whenever the group algebra $L^1(\bar{G})$ satisfies a spectral property which we call…

A locally compact group $G$ is compact if and only if $L^1(G)$ is an ideal in $L^1(G)^{**}$, and the Fourier algebra $A(G)$ of $G$ is an ideal in $A(G)^{**}$ if and only if $G$ is discrete. On the other hand, $G$ is discrete if and only if…