Related papers: Rigidity of multiparameter actions
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…
A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their applications to special function theory.
An algebraic $\Gamma$-action is an action of a countable group $\Gamma$ on a compact abelian group $X$ by continuous automorphisms of $X$. We prove that any expansive algebraic action of a finitely generated nilpotent group $\Gamma$ on a…
In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possible in modelling of molecular crystals, granular media, and…
In this survey, symmetry provides a framework for classification of manifolds with differential-geometric structures. We highlight pseudo-Riemannian metrics, conformal structures, and projective structures. A range of techniques have been…
We investigate group actions in which certain primitive elements fix a point, while not all group elements possess this property when acting upon some space. Using similar dynamical tools, we introduce the notion of Nielsen girth and prove…
We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…
We investigate the homotopy type of a certain homogeneous space for a simple complex algebraic group. We calculate some of its classical topological invariants and introduce a new one. We also propose several conjectures about its…
We consider two variants of those Abelian groups with all proper strongly invariant subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…
A new homological dimension is introduced to measure the quality of resolutions of `singular' finite dimensional algebras (of infinite global dimension) by `regular' ones (of finite global dimension). Upper bounds are established in terms…
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…
We give an upper bound on the number of the page on which the spectral sequence corresponding to a locally free isometric action of an abelian Lie group degenerates. We give examples showing that these bounds are indeed sharp. Finally, we…
We show that any action of a finite group on a finitely presentable group arises as the action of the group of self-homotopy equivalences of a space on its fundamental group. In doing so, we prove that any finite connected (abstract)…
We present some results on reductions and the copolarity of isometric group actions, which we obtained in our thesis. We also describe a resolution construction for isometric actions with respect to a reduction and give examples.
The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved in [4]. Later, this result was extended to all abelian groups [3] and, recently, to all torsion finitely quasihamiltonian groups [7].…
In the paper the algebra of invariants of the adjoint action of the unitriangular group in the nilradical of a parabolic subalgebra is studied. We set up a conjecture on the structure of the algebra of invariants. The conjecture is proved…
In recent contributions, algebraic multigrid methods have been designed and studied from the viewpoint of the spectral complementarity. In this note we focus our efforts on specific applications and, more precisely, on large linear systems…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.