Related papers: Higher generation by abelian subgroups in Lie grou…

For a connected Lie group G it was shown by Lee, Ludwig, Samei and Spronk that its Fourier algebra A(G) is weakly amenable only if G is abelian. We extend this result to general connected locally compact groups, extending an approach…

In this paper, we examine Lie group actions on moduli spaces (sets themselves built as quotients by group actions) and their fixed points. We show that when the Lie group is compact and connected, we obtain a linear constraint. This…

We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras integrates to a corresponding Lie group extension $\hat{G}$ of $G$ by $A$, where $G$ is a connected, simply connected Lie group and $A$ is a…

Let $G$ be a finite almost simple group with socle $G_0$. In this paper we prove that whenever $G/G_0$ is abelian, then there exists an abelian subgroup $A$ of $G$ such that $G=AG_0$. We propose a few applications of this structural…

In this note we show that the second homotopy group of $B(2,G)$, the classifying space for commutativity for a compact Lie group $G$, contains a direct summand isomorphic to $\pi_1(G)\oplus\pi_1([G,G])$, where $[G,G]$ is the commutator…

An element $g$ of a Lie group is called stably elliptic if it is contained in the interior of the set $G^e$ of elliptic elements, characterized by the property that $\mathrm{Ad}(g)$ generates a relatively compact subgroup. Stably elliptic…

A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and…

Let $G$ be the finite simple group of Lie type $G = E_7(q)$, where $q$ is an odd prime power. Then $G$ is an index $2$ subgroup of the adjoint group $G_{\operatorname{ad}}$, which is also denoted by $G_{\operatorname{ad}} =…

Let g=g_0+ g_1 be a simple Z_2-graded Lie algebra and let b_0 be a fixed Borel subalgebra of g_0. We describe and enumerate the abelian b_0-stable subalgebras of g_1.

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…

Let G be a compact connected Lie group. We prove that the Fourier algebra A(G) is weakly amenable if and only if G is abelian.

In this short note we prove that the finite non-abelian simple groups PSL(2,q), where q = 5,7, are determined by their posets of classes of isomorphic subgroups. In particular, this disproves the conjecture in the end of [5].

Let G and C be two discrete abelian groups. It is known that Pext(C,G) is a subgroup of Ext(C,G). In this paper, we introduce the t-extensions of G by C. We will show that the set of all t-extensions of G by C is a subgroup of Ext(C,G)…

Let $\gg$ be the Lie algebra of a compact Lie group and let $\theta$ be any automorphism of $\gg$. Let $\gk$ denote the fixed point subalgebra $\gg^\theta$. In this paper we present LiE programs that, for any finite dimensional complex…

An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian normal subgroup. The majority of 3-dimensional real Lie groups are almost Abelian, and they appear in all parts of physics that deal with anisotropic media…

In this paper we bring together results about the density of subsemigroups of abelian Lie groups, the minimal number of topological generators of abelian Lie groups and a result about actions of algebraic groups. We find the minimal number…

We study locally compact groups having all dense subgroups (locally) minimal. We call such groups densely (locally) minimal. In 1972 Prodanov proved that the infinite compact abelian groups having all subgroups minimal are precisely the…

Let $A$ be an abelian surface and let $G$ be a finite group of automorphisms of $A$ fixing the origin. Assume that the analytic representation of $G$ is irreducible. We give a classification of the pairs $(A,G)$ such that the quotient $A/G$…

We fill in the details in a procedure outlined by Serre for drawing pictures of compact real Lie groups. In the case of Sp($2n$), the picture generated by the method is connected with abelian varieties over a number field or a finite field.…

In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(\widetilde G) of its completion. Specifically, we characterize the pairs (C,A) of…