Almost set-theoretic complete intersections in characteristic zero.
We present a class of toric varieties V which, over any algebraically closed field of characteristic zero, are defined by codim V +1 binomial equations.
Almost totally projective groups
Almost Trivial Groupoids
Almost-Bieberbach groups with prime order holonomy
The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds. That is: we look for infra-nilmanifolds with prime order holonomy which can be obtained as a fiber space with a non-trivial nilmanifold as fiber and an infra-nilmanifold as its base. In this perspective, we prove the following algebraic result: if E is an almost-Bieberbach group with prime order holonomy,...
Almost-flat modules
We present general properties for almost-flat modules and we prove that a self-small right module is almost flat as a left module over its endomorphism ring if and only if the class of -static modules is closed under the kernels.
Almost-free E(R)-algebras and E(A,R)-modules
Let R be a unital commutative ring and A a unital R-algebra. We introduce the category of E(A,R)-modules which is a natural extension of the category of E-modules. The properties of E(A,R)-modules are studied; in particular we consider the subclass of E(R)-algebras. This subclass is of special interest since it coincides with the class of E-rings in the case R = ℤ. Assuming diamond ⋄, almost-free E(R)-algebras of cardinality κ are constructed for any regular non-weakly compact cardinal κ > ℵ...
A-loops close to code loops are groups
Let be a diassociative A-loop which is centrally nilpotent of class 2 and which is not a group. Then the factor over the centre cannot be an elementary abelian 2-group.
Alternating group coverings of the affine line for characteristic greater than two.
Amalgamated Free Products of Groups and Homological Duality
Amalgamated products and finitely presented groups.
Amalgams of free inverse semigroups.
Amalgams of torsion-free nilpotent groups of class three
Amenability and Ramsey theory
The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey-theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non-amenable group G, there is a subset E of G such that no finitely additive probability measure on G measures all translates of E equally. The analysis of discrete groups will be generalized to the setting...
Amenability of linear-activity automaton groups
We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.
Amenability properties of Figà-Talamanca-Herz algebras on inverse semigroups
This paper continues the joint work with A. R. Medghalchi (2012) and the author’s recent work (2015). For an inverse semigroup S, it is shown that has a bounded approximate identity if and only if l¹(S) is amenable (a generalization of Leptin’s theorem) and that A(S), the Fourier algebra of S, is operator amenable if and only if l¹(S) is amenable (a generalization of Ruan’s theorem).
Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property
We show that the amalgamated free products of two free groups over a cyclic subgroup admit amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on two generators.
Amenable actions of nonamenable groups.
Amenable group actions on infinite graphs.
Amenable groups and cellular automata
We show that the theorems of Moore and Myhill hold for cellular automata whose universes are Cayley graphs of amenable finitely generated groups. This extends the analogous result of A. Machi and F. Mignosi “Garden of Eden configurations for cellular automata on Cayley graphs of groups” for groups of sub-exponential growth.
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...