Related papers: Topological groups with invariant linear spans

We define the notion of strong spectral invariance for a dense Frechet subalgebra A of a Banach algebra B. We show that if A is strongly spectral invariant in a C*-algebra B, and G is a compactly generated polynomial growth Type R Lie…

If $R$ is a topological ring then $R^{\ast}$, the group of units of $R$, with the subspace topology is not necessarily a topological group. This leads us to the following natural definition: By an \emph{absolute topological ring} we mean a…

For any finitely generated, non-elementary, torsion-free group $G$ that is hyperbolic relative to $\mathbb P$, we show that there exists a group $G^*$ containing $G$ such that $G^*$ is hyperbolic relative to $\mathbb P$ and $G$ is not…

Suppose that $\{T_{a}:a\in G\}$ is a group of uniformly $L$-Lipschitzian mappings with bounded orbits $\left\{T_{a}x:a\in G\right\}$ acting on a hyperconvex metric space $M$. We show that if $L<\sqrt{2}$, then the set of common fixed points…

Sunada's work on crystallography emphasizes the role of the "maximal abelian cover" of a graph $X$. This is a covering space of $X$ for which the group of deck transformations is the first homology group $H_1(X,\mathbb{Z})$. An embedding of…

A multiple group rack is a rack which is a disjoint union of groups equipped with a binary operation satisfying some conditions. It is used to define invariants of spatial surfaces, i.e., oriented compact surfaces with boundaries embedded…

Let $Aut_{alg}(X)$ be the subgroup of the group of regular automorphisms $Aut(X)$ of an affine algebraic variety $X$ generated by all connected algebraic subgroups. We prove that if $dim X \ge 2$ and if $Aut_{alg}(X)$ is rich enough,…

Associated to each finite dimensional linear representation of a group G, there is a vector bundle over the classifying space BG. This construction was studied extensively for compact groups by Atiyah and Segal. We introduce a homotopy…

An algebra group over a field $F$ is a group of the form $G = 1+J$ where $J$ is a finite-dimensional nilpotent associative $F$-algebra. A theorem of M. Boyarchenko asserts that, in the case where $F$ is a non-archimedean local field, every…

We generalise the definition of a group algebra so that it makes sense for non-locally compact topological groups, in particular, we require that the representation theory of the group algebra is isomorphic (in the sense of Gelfand-Raikov)…

In this note we introduce the notion of a transcendental group, that is, a subgroup $G$ of the topological group $\mathbb{C}$ of all complex numbers such that every element of $G$ except $ 0$ is a transcendental number. All such topological…

Let $G$ be an amenable group. We define and study an algebra $\mathcal{A}_{sn}(G)$, which is related to invariant means on the subnormal subgroups of $G$. For a just infinite amenable group $G$, we show that $\mathcal{A}_{sn}(G)$ is…

Strongly zero-dimensional topological groups $G_1$, $G_2$, and $G$ such that $G_1\times G_2$ has positive covering dimension and $G$ contains a closed subgroup of positive covering dimension are constructed. Moreover, all finite powers of…

We prove that the mapping stack Map(Y,X) of topological stacks X and Y is again a topological stack if Y admits a compact groupoid presentation. If Y admits a locally compact groupoid presentation, we show that Map(Y,X) is a paratopological…

We present a method to compute the group of affine transformations of a homogeneous $G$-space under specific conditions: when the group $G$ and the homogeneous $G$-space admit linear connections so that the natural projection is affine, and…

Let G be a Lie group and E be a locally convex topological G-module. If E is sequentially complete, then E and its space of smooth vectors are modules for the algebra D(G) of compactly supported smooth functions on G. However, the module…

We show that all groups of a distinguished class of \guillemotleft large\guillemotright\ topological groups, that of Roelcke precompact Polish groups, have Kazhdan's Property (T). This answers a question of Tsankov and generalizes previous…

We study the category of wheeled PROPs using tools from Invariant Theory. A typical example of a wheeled PROP is the mixed tensor algebra ${\mathcal V}=T(V)\otimes T(V^\star)$, where $T(V)$ is the tensor algebra on an $n$-dimensional vector…

A topological space $X$ is defined to have a neighborhood $P$-base at any $x\in X$ from some poset $P$ if there exists a neighborhood base $(U_p[x])_{p\in P}$ at $x$ such that $U_p[x]\subseteq U_{p'}[x]$ for all $p\geq p'$ in $P$. We prove…

The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural distance on the space of compact open subgroups of G. For a…