Related papers: Pointwise-relatively-compact subgroups and trivial…
A surface group representation into a Lie group is called totally elliptic if every simple closed curve on the surface is mapped to an elliptic element of the target group. In this note, we characterize all totally elliptic surface group…
We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product of a topological group over topological spaces with a continuous sandwich function. We prove that a simple topological semigroup $S$ is…
Let $\ell$ be a prime. If ${\mathbf G} $ is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from $\ell$, and $\ell$ is a good prime for ${\mathbf G}$, we show that the number of weights of…
A semisimple algebraic tensor category over an algebraically closed field k of characteristic zero is the representation category of all finite dimensional twisted super representations of an affine reductive supergroup G over k. Such a…
We prove that any countable discrete and torsion free subgroup of a general linear group over an arbitrary field or a similar subgroup of an almost connected Lie group satisfies the integral algebraic K-theoretic (split) Novikov conjecture…
The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple three-dimensional group is considered. An upper bound is…
A generalized Euler parameterization of a compact Lie group is a way for parameterizing the group starting from a maximal Lie subgroup, which allows a simple characterization of the range of parameters. In the present paper we consider the…
We continue in this paper the study of locally minimal groups started in \cite{LocMin}. The minimality criterion for dense subgroups of compact groups is extended to local minimality. Using this criterion we characterize the compact abelian…
We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…
We study topological groups having all closed subgroups (totally) minimal and we call such groups c-(totally) minimal. We show that a locally compact c-minimal connected group is compact. Using a well-known theorem of Hall and Kulatilaka…
The concept of a C-approximable group, for a class of finite groups C, is a common generalization of the concepts of a sofic, weakly sofic, and linear sofic group. Glebsky raised the question whether all groups are approximable by finite…
We consider linear groups and Lie groups over a non-Archimedean local field $\mathbb F$ for which the power map $x\mapsto x^k$ has a dense image or it is surjective. We prove that the group of $\mathbb F$-points of such algebraic groups is…
An argument of A.Borel shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an…
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…
The rank rk(G) of a profinite group G is the supremum of d(H), where H ranges over all closed subgroups of G and d(H) denotes the minimal cardinality of a topological generating set for H. A compact topological group G admits the structure…
It is proved that, for a wide class of topological abelian groups (locally quasi--convex groups for which the canonical evaluation from the group into its Pontryagin bidual group is onto) the arc component of the group is exactly the union…
We ask a general question: what are locally homogeneous compact pseudo-Riemannian Einstein manifolds? We show that any standard compact Clifford-Klein form of a simple non-compact Lie group admits at least one Einstein metric. We conjecture…
Hrushovski proved the Lie model theorem in full generality with model theoretic methods. The theorem states that for every approximate group there exists a generalized definable locally compact model, which, simplifying, is a…
The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized…
The article is about an elliptic problem defined on a {\it stratified Lie group}. Both sub- and superlinear cases are considered whose solutions are guaranteed to exist in light of the interplay between the nonlinearities and the weak $L^1$…