Related papers: Conjugacy class conditions in locally compact seco…

We extend the 2-representation theory of finitary 2-categories to certain 2-categories with infinitely many objects, denoted locally finitary 2-categories, and extend the classical classification results of simple transitive…

We show that conjugacy of reversible cellular automata is undecidable, whether the conjugacy is to be performed by another reversible cellular automaton or by a general homeomorphism. This gives rise to a new family of finitely-generated…

We embed a countably categorical group G into a locally compact group c(G) with a non-trivial topology and study how topological properties of c(G) are connected with the structure of definable subgroups of G.

For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open)…

Analytic properties of right topological groups have been extensively studied in the compact admissible case (i.e when the group has a dense topological center). This was inspired by the existence of a Haar measure on such groups. In this…

In this short note we construct two countable, infinite conjugacy class groups which admit free, ergodic, probability measure preserving orbit equivalent actions, but whose group von Neumann algebras are not (stably) isomorphic.

We prove a rank-two potential automorphy theorem for mod $l$ representations satisfying an ordinary condition. Combined with an ordinary automorphy lifting theorem, we prove a rank-two, $p \ne l$ case of local-global compatibility for…

A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that $\eta_i:\X_i\to \X_i$ is a continuous proper map on a locally compact…

We show that basic notions of locally analytic representation theory can be reformulated in the language of topological coalgebras (Hopf algebras) and comodules. We introduce the notion of admissible comodule and show that it corresponds to…

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on…

Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally…

In this paper we classify the finite groups satisfying the following property $P_4$: their orders of representatives are set-wise relatively prime for any 4 distinct non-central conjugacy classes.

We motivate and study the class $\mathcal{C}$ of countable groups $G$ such that the conjugacy relation between minimal actions of $G$ on $\mathbb{R}$ by orientation-preserving homeomorphisms is smooth -- that is, admits a Borel transversal.…

We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove that if the equivalence relation of isomorphism is potentially…

We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively unform-, order-, and $\sigma$-order convergence,…

If k is an arbitrary field, we construct a category of k-1-motives in which every commutative algebraic k-group G has a dual object $G^{\vee}$. When k is a local field of arbitrary characteristic, we establish Pontryagin duality theorems…

The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…

Let ${\cal C}$ be a nonempty class of finite groups closed under taking subgroups, homomorphic images and extensions. A subgroup $H$ of an abstract residually ${\cal C}$ group $R$ is said to be conjugacy ${\cal C}$-distinguished if whenever…

We undertake a comprehensive study of measure equivalence between general locally compact, second countable groups, providing operator algebraic and ergodic theoretic reformulations, and complete the classification of amenable groups within…

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…