相关论文: Rigidity of multiparameter actions

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.

In the present paper we study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either…

The equivariant cohomology for actions of compact connected abelian groups and elementary abelian p-groups have been widely studied in the last decades. We study some of these results on actions of finite cyclic groups over a field of…

The study of actions of countable groups by automorphisms of compact abelian groups has recently undergone intensive development, revealing deep connections with operator algebras and other areas. The discrete Heisenberg group is the…

We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…

In this article we discuss relations between algebraic and dynamical properties of non-cyclic semigroups of rational maps.

We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.

The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments…

This paper is devoted to a systematic study of the geometry of nondegenerate $\bbR^n$-actions on $n$-manifolds. The motivations for this study come from both dynamics, where these actions form a special class of integrable dynamical systems…

Proper group actions are ubiquitous in mathematics and have many of the attractive features of actions of compact groups. In this survey, we discuss proper actions of Lie groups on smooth manifolds. If the group dimension is sufficiently…

We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally…

We report on recent progress concerning the relationship that exists between the algebraic structure of a finite group and certain features of its class-size prime graph.

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…

We study Poisson valuations and provide their applications in solving problems related to rigidity, automorphisms, Dixmier property, isomorphisms, and embeddings of Poisson algebras and fields.

Relations between parameter rigidity of locally free Lie group actions on closed manifolds and the 1st leafwise cohomology of the orbit foliations are discussed. Some computational results of the leafwise cohomology are included.

We explore the rigidity of generic frameworks in 3-dimensions whose underlying graph is close to being planar. Specifically we consider apex graphs, edge-apex graphs and their variants and prove independence results in the generic…

We study the behaviour of the topological fundamental group under totally ramified abelian covers (a special case of abelian Galois covers) of complex projective varieties of dimension at least 2.

This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially,…