Related papers: Local indicability of groups with homology circle …
In group representations several inductions given by tensoring with appropriate bimodules may be reconstructed via homology of $G$-posets with $G$-equivariant coefficients. For this purpose, we need various local categories of a finite…
Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact sigma-compact…
We define and study the invariant linear and nonlinear horizontal double complexes of a local Lie group.
In this paper, we consider homology groups induced by the exterior algebra generated by a simplicial compliment of a simplicial complex $K$. These homology groups are isomorphic to the Tor-groups $\mathrm{Tor}_{i,…
This paper consists of two parts. In the first part we show that any Poisson algebraic group over a field of characteristic zero and any Poisson Lie group admits a local quantization. This answers positively a question of Drinfeld. In the…
The notion of local equivalence relation on a topological space is generalised to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation…
In this paper we continue the study of locally analytic representations of a $p$-adic Lie group $G$ in vector spaces over a spherically complete non-archimedean field $K$, building on the algebraic approach to such representations…
We calculate the local cyclic homology of group Banach-algebras of discrete groups acting properly, isometrically and cocompactly on a CAT(0)-space.
We propose a unified framework in which the different constructions of cohomology groups for topological and Lie groups can all be treated on equal footings. In particular, we show that the cohomology of "locally continuous" cochains…
A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
We combine harmonic analysis and operator algebraic techniques to give a concise argument that the left regular representation of a locally compact group is cyclic if and only if the group is first countable, a result first proved by…
We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of…
We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the…
We discuss the question whether left-orderable groups satisfying a nontrivial law are locally indicable.
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on any sets with asymptotic density with respect to a specific norm. We…
We use the abstract framework constructed in our earlier paper to study local duality for Noetherian $\mathbb{E}_{\infty}$-ring spectra. In particular, we compute the local cohomology of relative dualizing modules for finite morphisms of…
We introduce higher-order support varieties for pairs of modules over a commutative local complete intersection ring, and give a complete description of which varieties occur as such support varieties. In the context of a group algebra of a…
We introduce a local version of contact homology for an isolated periodic orbit of the Reeb flow and prove that its rank is uniformly bounded for isolated iterations. Several applications are obtained, including a generalization of…
The Tate conjecture has two parts: i) Tate classes are linear combination of algebraic classes, ii) semisimplicity of Galois representations (for smooth projective varieties). B. Moonen proved that i) implies ii) in characteristic 0, using…