Related papers: L^2-Betti numbers of coamenable quantum groups

Consider a C*-algebra $A$ with a comultiplication $\Delta$. This pair is usually thought of as locally compact quantum semi-group. When these notes were written, in 1993, it was not at all clear what the extra assumptions on the…

Let $\mathbb{G}$ be a compact quantum group and $A\subseteq B$ an inclusion of $\sigma$-finite $\mathbb{G}$-dynamical von Neumann algebras. We prove that the $\mathbb{G}$-inclusion $A\subseteq B$ is strongly equivariantly amenable if and…

Let $U_\zeta$ be the quantum group (Lusztig form) associated to the simple Lie algebra $\mathfrak{g}$, with parameter $\zeta$ specialized to an $\ell$-th root of unity in a field of characteristic $p>0$. In this paper we study certain…

In this article, we give a class of examples of compact quantum groups and unitary 2-cocycles on them, such that the twisted quantum groups are non-compact, but still locally compact quantum groups (in the sense of Kustermans and Vaes).…

We examine a condition on a simply connected 2-complex X ensuring that groups acting properly on X are coherent. This extends earlier work on 2-complexes with negative sectional curvature which covers the case that G acts freely. Our…

We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic reflection algebras and graded Hecke algebras to the…

This paper gives a complete selfcontained proof of our result announced in hep-th/9909126 showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on…

In this series of papers, we develop the theory of a class of locally compact quantum groupoids, which is motivated by the purely algebraic notion of weak multiplier Hopf algebras. In this Part I, we provide motivation and formulate the…

For a Banach algebra $A$ with a bounded approximate identity, we investigate the $A$-module homomorphisms of certain introverted subspaces of $A^*$, and show that all $A$-module homomorphisms of $A^*$ are normal if and only if $A$ is an…

Andreotti-Vesentini, Ohsawa, Gromov, Koll\'ar, among others, have observed that Hodge theory could be extended to (non compact) K\"ahler complete manifolds, within the L^2 framework. Also, many vanishing theorems on projective or K\"ahler…

We show that for any compact connected group G the second cohomology group defined by unitary invariant 2-cocycles on \hat G is canonically isomorphic to H^2(\hat{Z(G)};T). This implies that the group of autoequivalences of the C*-tensor…

We prove that the canonical dimension of a coadmissible representation of a semisimple $p$-adic Lie group in a $p$-adic Banach space is either zero or at least half the dimension of a non-zero coadjoint orbit. To do this we establish…

In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the…

This thesis is devoted to the study of Lie bialgebra and Hopf algebra structures related to certain versions of non-commutative geometry constructed on infinite-dimensional Lie algebras that arise in the context of asymptotic symmetries of…

We define for arbitrary modules over a finite von Neumann algebra $\cala$ a dimension taking values in $[0,\infty]$ which extends the classical notion of von Neumann dimension for finitely generated projective $\cala$-modules and inherits…

We prove a Kunneth formula computing the Connes-Shlyakhtenko L^2-Betti numbers of the algebraic tensor product of two tracial *-algebras in terms of the L^2-Betti numbers of the two original algebras. As an application, we construct…

The purpose of this paper is to generalise Sullivan's rational homotopy theory to non-nilpotent spaces, providing an alternative approach to defining Toen's schematic homotopy types over any field k of characteristic zero. New features…

We investigate homological and ring-theoretic properties of universal quantum linear groups that coact on Artin-Schelter regular algebras A(n) of global dimension 2, especially with central homological codeterminant (or central quantum…

This paper provides a systematic study of the operational idea that a quantum ``state'' is only defined up to what can be distinguished by a chosen family of observables. Concretely, any von Neumann algebra of observables $\mathscr{M}$…

We provide a proof for an inequality between volume and L2-Betti numbers of aspherical manifolds for which Gromov outlined a strategy based on general ideas of Connes. The implementation of that strategy involves measured equivalence…