Related papers: Local indicability of groups with homology circle …

In this paper, we define locally matchable subsets of a group which is extracted from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…

We investigate weakly $G$-slim complexes, a more flexible variant of Helfer and Wise's slim complexes, which can be defined on any regular $G$-covering. We prove that if a $2$-complex $X$ associated to a group presentation is weakly…

We show that a Hamiltonian in terms of the local real-space currents obeying an $\mathfrak{su}_1(2)$ affine Lie algebra eliminates the non-locality in the Hatsugai-Kohmoto model for a doped Mott insulator. We establish this local…

This is an old paper put here for archeological purposes. We derive a general formula expressing the second homology of a Lie algebra of the form L\otimes A with coefficients in the trivial module through homology of $L$, cyclic homology of…

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

Local log-regular rings are a certain class of Cohen-Macaulay local rings that are treated in logarithmic geometry. Our paper aims to provide purely commutative ring theoretic proof of some ring-theoretic properties of local log-regular…

A pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this note we show that a pro-Lie group $G$ is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the…

The closed string model in the background gravity field is considered as the bi-Hamiltonian system in assumption that string model is the integrable model for particular kind of the background fields. The dual nonlocal Poisson brackets, de…

Viewing higher local fields as ring objects in the category of iterated pro-ind-objects, a definition of open subgroups in Milnor K-groups of the fields is given. The self-duality of the additive group of a higher local field is proved. By…

We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This…

In [7], results about the global Jacquet-Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field are…

We study a class of two-generator two-relator groups, denoted $J_n(m,k)$, that arise in the study of relative asphericity as groups satisfying a transitional curvature condition. Particular instances of these groups occur in the literature…

A homology cylinder over a compact manifold is a homology cobordism between two copies of the manifold together with a boundary parametrization. We study abelian quotients of the homology cobordism group of homology cylinders. For homology…

In this thesis, two $\bar{\mathbb{Q}}_\ell$-local systems, $\vphantom{\mathcal{E}}^\circ \mathcal{E}$ and $\vphantom{E}^\circ \mathcal{E}^\prime$ on the regular unipotent subvariety $\mathcal{U}_{0,K}$ of $p$-adic $\operatorname{SL}_2(K)$…

We prove the Baum--Connes conjecture with arbitrary coefficients for some classes of groups: (1) Linear algebraic groups over a non-archimedean local field. (2) Linear algebraic groups over the adeles of a global field k, provided that at…

We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group $N$, there is a one-to-one correspondence between the set of isomorphism classes of connected Lie…

For locally compact groups, we define an analogue to Yu's property A that he defined for discrete metric spaces. We show that our property A for locally compact groups agrees with Roe's notion of property A for proper metric spaces, defined…

We study analogues of Cartan decompositions of Lie groups for totally disconnected locally compact groups. It is shown using these decompositions that a large class of totally disconnected locally compact groups acting on trees and…

In the present paper we study abelian extensions of connected Lie groups $G$ modeled on locally convex spaces by smooth $G$-modules $A$. We parametrize the extension classes by a suitable cohomology group $H^2_s(G,A)$ defined by locally…

We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group $G$ associated with non-singular $G$-spaces. We deduce that any two boundary representations of a…