Related papers: Examples of descent up to nilpotence

We consider ordered tuples in finite groups generating nilpotent subgroups. Given an integer $q$ we consider the poset of nilpotent subgroups of class less than $q$ and its corresponding coset poset. These posets give rise to a family of…

We present two examples of actions of non-regular locally compact quantum groups on their homogeneous spaces. The homogeneous spaces are defined in a way specific to these examples, but the definitions we use have the advantage of being…

The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for…

In this paper, we present recent results about the developement of a semiclassical approach in the setting of nilpotent Lie groups and nilmanifolds. We focus on two-step nilmanifolds and exhibit some properties of the weak limits of…

For any finite group $G$, we define the notion of a Bredon homotopy action of $G$, modelled on the diagram of fixed point sets $(X_H)_{H\leq G}$ for a $G$-space $X$, together with a pointed homotopy action of the group $N_{G}H/H$ on…

Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend to homotopy colimits of 2-functors lower categorical…

In this note, it is shown that the nilpotency of submatrices of a certain class of adjacency matrices is equivalent to the aperiodic Collatz conjecture.

We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions. Moreover, a combinatorial…

We draw a connection between the model-theoretic notions of modularity (or one-basedness), orthogonality and internality, as applied to difference fields, and questions of descent in in algebraic dynamics. In particular we prove in any…

In this talk, I will survey recent progress made on the classification of von Neumann algebras arising from countable groups and their actions on probability spaces. In particular, I will present the first results which provide classes of…

We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong…

We consider the finest grading of the algebra of regular functions of a trinomial variety. An explicit description of locally nilpotent derivations that are homogeneous with respect to this grading is obtained.

Hilbert evolution algebras generalize evolution algebras through a framework of Hilbert spaces. In this work we focus on infinite-dimensional Hilbert evolution algebras and their representation through a suitably defined weighted digraph.…

For a finite group $G$ and a non-negative integer $d$, denote by $\Omega_d(G)$ the number of functions $G^d\rightarrow G$ that are induced by substitution into a word with variables among $X_1,\ldots,X_d$. In this note, we show that…

Let A be an associative algebra of arbitrary dimension over a field F and G a finite soluble group of automorphisms of A oforder n, prime to the characteristic of F. We prove that if the fixed-point subalgebra of A under the action of G…

We give an estimate of the number $N(\lambda)$ of eigenvalues $<\lambda$ for the image under an irreducible representation of the ``sublaplacian'' on a stratified nilpotent Lie algebra. We also give an estimate for the trace of the…

We consider a class of finite-dimensional algebras, the so-called "Staircase algebras" parametrized by Young diagrams. We develop a complete classification of representation types of these algebras and look into finite, tame (concealed) and…

We study the theory of convergence for CAT$(0)$-lattices (that is groups $\Gamma$ acting geometrically on proper, geodesically complete CAT$(0)$-spaces) and their quotients (CAT$(0)$-orbispaces). We describe some splitting and collapsing…

In this paper we give an attempt to extend some arithmetic properties such as multiplicativity, convolution products to the setting of operators theory. We provide a significant examples which are of interest in number theory. We also give…

Using Gillet's technique of projective envelopes, we prove a homological descent theorem for the connective K-homology of schemes.