Related papers: Finite presentation, the local lifting property, a…

The present article deals with the local approximation results by means of Lipschitz maximal function, Ditzian-Totik modulus of smoothness and Lipschitz type space having two parameters for the summation-integral type operators defined by…

Let $G$ be a semisimple Lie group with finite component group, and let $K<G$ be a maximal compact subgroup. We obtain a quantisation commutes with reduction result for actions by $G$ on manifolds of the form $M = G\times_K N$, where $N$ is…

This survey is about old and new results about the modular representation theory of finite reductive groups with a strong emphasis on local methods. This includes subpairs, Brauer's Main Theorems, fusion, Rickard equivalences. In the…

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

We introduce the spatial Rokhlin property for actions of coexact compact quantum groups on $\mathrm{C}^*$-algebras, generalizing the Rokhlin property for both actions of classical compact groups and finite quantum groups. Two key…

We prove a number of property (T) permanence results for locally compact quantum groups under exact sequences and the presence of invariant states, analogous to their classical versions. Along the way we characterize the existence of…

We introduce a local homology theory for linearly compact modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties such as the noetherianness, the vanishing and non-vanishing of local…

Let $B$ be a Banach $A-bimodule$ and let $n\geq 0$. We investigate the relationships between some cohomological groups of $A$, that is, if the topological center of the left module action $\pi_\ell:A\times B\rightarrow B$ of $A^{(2n)}$ on…

We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…

The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.

We prove several structural results on definably compact groups G in o-minimal expansions of real closed fields, such as (i) G is definably an almost direct product of a semisimple group and a commutative group, and (ii) the group (G, .) is…

We show that every finitely generated group admits weak analogues of an invariant expectation, whose existence characterizes exact groups. This fact has a number of applications. We show that Hopf $G$-modules are relatively injective, which…

The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks 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…

Let $Y$ be a CW-complex with a single 0-cell, $K$ its Kan group, a model for the loop space of $Y$, and let $G$ be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant…

We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields…

We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…

We introduce Hecke algebras associated to discrete quantum groups with commensurated quantum subgroups. We study their modular properties and the associated Hecke operators. In order to investigate their analytic properties we adapt the…

The following paper is devoted to the study of type I locally compact quantum groups. We show how various operators related to the modular theory of the Haar integrals on $\mathbb{G}$ and $\widehat{\mathbb{G}}$ act on the level of direct…

For a topological group $G$, amenability can be characterized by the amenability of the convolution Banach algebra $L^1(G)$. Here a Banach algebra $A$ is called amenable if every bounded derivation from $A$ into any dual--type…