We show that in the semiclassical limit the eigenfunctions of quantized ergodic symplectic toral automorphisms cannot concentrate in measure on closed orbits of the dynamics. More generally, we show that the mass of the pure point component of the limit measure must be smaller than two thirds of the total mass. The proofs use only the algebraic (i.e., not the number-theoretic) properties of the...

It has been asserted that any (full) order on a torsion-free, finitely generated, nilpotent group is defined by some F-basis of G and that the group of o-automorphisms of such a group is itself a group of the same kind: Examples provided herein demonstrate that both of these assertions are false; however, it is proved that the group of o-automorphisms of an ordered, polycyclic group is nilpoten...

Using n finite order automorphisms on a simple complex Lie algebra we construct twisted n-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case n = 2 we list certain simple Lie algebras and their automorphisms, which produce twisted 2-toroidal algebras. In this way we obtain Lie algebras that are related to all Extended Affine Root Systems of K. Sa...

I report an error in Theorem A of Automorphisms of free groups. I , New York J. Math. 19 (2013), 395–421, where it was claimed that two filtrations of the group of IA automorphisms of a free group coincide up to torsion. In fact, using a recent result by Day and Putman, I show that, for a free group of rank 3, the opposite conclusion holds, namely that the two series differ rationally.

There are described some algebraic structures on a space of belief functions on a two element frame namely so called Dempster s semigroup with Dempster s operation dempsteroids and their basic properties The present paper is devoted to the investi gation of automorphisms of Dempster s semigroup Full characterization of general and ordered automorphisms is obtained their parametric description i...

Let G be a profinite group and let α be an automorphism of G. Then α is topologically intense if, for every closed subgroup H of G, there exists x ∈ G such that α(H) = xHx. Topologically intense automorphisms are automatically continuous, because they stabilize each open normal subgroup of the group on which they are defined. We denote by Intc(G) the group of topologically intense automorphisms...

Abstract We prove sharp upper and lower bounds for generalized Calderón’s sums associated to frames on LCA groups generated by affine actions of cocompact subgroup translations and general measurable families of automorphisms. The proof makes use of techniques of analysis on metric spaces, and relies on a counting estimate of lattice points inside metric balls. We will deduce as special cases C...

In this paper, given a split extension of an arbitrary Coxeter group by automorphisms of the Coxeter graph, we determine the involutions in that extension whose centralizer has finite index. Our result has applications to many problems such as the isomorphism problem of general Coxeter groups. In the argument, some properties of certain special elements and of the fixed-point subgroups by graph...

We study mixing properties of epimorphisms of a compact connected finite-dimensional abelian group X . In particular, we show that a set F , |F | > dimX , of epimorphisms of X is mixing iff every subset of F of cardinality (dimX)+1 is mixing. We also construct examples of free nonabelian groups of automorphisms of tori which are mixing, but not mixing of order 3, and show that, under some irred...

We show that the dynamics of automorphisms on all projective complex manifolds X (of dimension 3, or of any dimension but assuming the Good Minimal Model Program or Mori’s Program) are canonically built up from the dynamics on just three types of projective complex manifolds: complex tori, weak Calabi-Yau manifolds and rationally connected manifolds. As a by-product, we confirm the conjecture o...