Related papers: Linear dynamical systems of nilpotent Lie groups

In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor)…

In these lectures we consider how algebraic properties of discrete subgroups of Lie groups restrict the possible actions of those groups on surfaces. The results show a strong parallel between the possible actions of such a group on the…

The present paper is the third contribution of a series of works, where we investigate pseudo--bosonic operators and their connections with finite dimensional Lie algebras. We show that all finite dimensional nilpotent Lie algebras (over…

A Lie algebra is called nonsoliton if it does not admit a soliton inner product. We demonstrate that the subset of nonsoliton Lie algebras in the moduli space of indecomposable n-dimensional N-graded nilpotent Lie algebras is discrete if…

A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…

We study the diophantine exponent of analytic submanifolds of the space of m by n real matrices, answering questions of Beresnevich, Kleinbock and Margulis. We identify a family of algebraic obstructions to the extremality of such a…

We study the geodesic orbit property for nilpotent Lie groups $N$ when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When $N$ acts on itself by…

We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert $C^*$-module either is closable or has a dense range. We also describe dynamical systems on a full Hilbert $C^*$-module ${\mathcal M}$…

We give a classification of normal affine surfaces admitting an algebraic group action with an open orbit. In particular an explicit algebraic description of the affine coordinate rings and the defining equations of such varieties is given.…

We define a class of Riemannian and pseudo-Riemannian 2-step nilpotent Lie groups with nondegenerate centers that generalize the H-type groups of Kaplan. Examples are given and geometric properties are investigated.

We study model geometries of finitely generated groups. If a finitely generated group does not contain a non-trivial finite rank free abelian commensurated subgroup, we show any model geometry is dominated by either a symmetric space of…

Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset…

We study internal Lie algebras in the category of subshifts on a fixed group -- or Lie algebraic subshifts for short. We show that if the acting group is virtually polycyclic and the underlying vector space has dense homoclinic points, such…

A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The C*-algebra generated by the partial isometries is thus a quotient of…

This paper is a study of the Lie groups of point symmetries admitted by a system describing a non-stationary planar flow of an ideal plastic material. For several types of forces involved in the system, the infinitesimal generators which…

A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of the Stone-Cech compactification of the natural numbers, or it…

Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the…

We introduce dynamic asymptotic dimension, a notion of dimension for actions of discrete groups on locally compact spaces, and more generally for locally compact \'etale groupoids. We study our notion for minimal actions of the integer…

We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…

For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…