Related papers: Acceptable compact Lie groups

For a compact convex subset K with non-empty interior in a finite-dimensional vector space, let G be the group of all smooth diffeomorphisms of K which fix the boundary of K pointwise. We show that G is a C^0-regular infinite-dimensional…

We obtain some general results on Sasakian Lie algebras and prove as a consequence that a (2n + 1)-dimensional nilpotent Lie group admitting left-invariant Sasakian structures is isomorphic to the real Heisenberg group $H_{2n + 1}$.…

Given a result of Herman, we provide a new elementary proof of the fact that the connected component of the group of compactly supported diffeomorphisms is perfect and hence simple. Moreover, we show that every diffeomorphism $g$, which is…

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 are interested in the class, in the Elie Cartan sense, of left invariant forms on a Lie group. We construct the class of Lie algebras provided with a contact form and classify the frobeniusian Lie algebras up to a contraction. We also…

If $G$ is a compact Lie group endowed with a left invariant metric $g$, then $G$ acts via pullback by isometries on each eigenspace of the associated Laplace operator $\Delta_g$. We establish algebraic criteria for the existence of left…

Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $\Sigma$ of genus $l >1$, the order of the group $H^2(\Sigma,\pi_1(G))$ is equal to the number of connected components of the…

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…

Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…

The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups $B_u(Q)$ for…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

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 obtain a Lie theoretic intrinsic characterization of the connected and simply connected solvable Lie groups whose regular representation is a factor representation. When this is the case, the corresponding von Neumann algebras are…

We say that an action of a countable discrete inverse semigroup on a locally compact Hausdorff space is amenable if its groupoid of germs is amenable in the sense of Anantharaman-Delaroche and Renault. We then show that for a given inverse…

Suppose that a finite group $G$ admits an automorphism $\varphi $ of order $2^n$ such that the fixed-point subgroup $C_G(\varphi ^{2^{n-1}})$ of the involution $\varphi ^{2^{n-1}}$ is nilpotent of class $c$. Let $m=|C_G(\varphi)|$ be the…

Let $G$ be a connected, simply-connected, compact simple Lie group. In this paper, we show that the isometry group of $G$ with a left-invariant pseudo-Riemannan metric is compact. Furthermore, the identity component of the isometry group is…

In part I we introduced the class ${\mathcal E}_2$ of Lie subgroups of $Sp(2,\R)$ and obtained a classification up to conjugation (Theorem 1.1). Here, we determine for which of these groups the restriction of the metaplectic representation…

We investigate closure results for C-approximable groups, for certain classes C of groups with invariant length functions. In particular we prove, each time for certain (but not necessarily the same) classes C that (i) the direct product of…

A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations of the Lie group. The problem of finding…

We study the existence of invariant metrics with holonomy $G_{2(2)}^* \subset SO(4,3)$ on compact nilmanifolds, i.e. on compact quotients of nilpotent Lie groups by discrete subgroups. We prove that, up to isomorphism, there exists only one…