相关论文: No representation of Moore groups and affine group…

Stressing the role of dual coalgebras, we modify the definition of affine schemes over the 'field with one element'. This clarifies the appearance of Habiro-type rings in the commutative case, and, allows a natural noncommutative…

We show that a compact group $G$ has finite conjugacy classes, i.e., is an FC-group if and only if its center $Z(G)$ is open if and only if its commutator subgroup $G'$ is finite. Let $d(G)$ denote the Haar measure of the set of all pairs…

The Poisson boundary of a finite direct product of affine automorphism groups of homogeneous trees is considered. The Poisson boundary is shown to be a product of ends of trees with a hitting measure for spread-out, aperiodic measures of…

We study a class of discrete-time random dynamical systems with compact phase space. Assuming that the deterministic counterpart of the system in question possesses a dissipation property, its linearisation is approximately controllable,…

We study the mapping class group of a nontrivial irreducible shift of finite type: the group of flow equivalences of its mapping torus modulo isotopy. This group plays for flow equivalence the role that the automorphism group plays for…

Let $G$ be a semi-direct product $G=A\times_\phi K$ with $A$ Abelian and $K$ compact. We characterize spread-out probability measures on $G$ that are mixing by convolutions by means of their Fourier transforms. A key tool is a spectral…

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

Let $(X,G)$, $(Y,G)$ be two $G$-systems, where $G$ is an infinite countable discrete amenable group and $X$, $Y$ are compact metric spaces. Suppose that $\mathcal{U}$ is a cover of $X$. We first introduce the conditional local topological…

We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…

We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…

We extend our previous study of Markov chains on finite commutative rings (arXiv:1605.05089) to arbitrary finite rings with identity. At each step, we either add or multiply by a randomly chosen element of the ring, where the addition…

A group $G$ has $FW_n$ if every action on a $n$-dimensional $\mathrm{CAT}(0)$ cube complex has a global fixed point. This provides a natural stratification between Serre's $FA$ and Kazhdan's $(T)$. For every $n$, we show that random groups…

We present a new criterion, based on commutator methods, for the strong mixing property of unitary representations of topological groups equipped with a proper length function. Our result generalises and unifies recent results on the strong…

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…

On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg…

Let $G$ be a countable group and $\mu$ a probability measure on $G$. We build a new framework to compute asymptotic quantities associated with the $\mu$-random walk on $G$, using methods from harmonic analysis on groups and Banach space…

This report is an account of freely representable groups, which are finite groups admitting linear representations whose only fixed point for a nonidentity element is the zero vector. The standard reference for such groups is Wolf (1967)…

We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps $T_\alpha$ using the full parameter range $0<…

An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all…

Let $\mu$ be a finitely supported probability measure on the group of automorphisms of $\mathbb{A}^2_\mathbb{C}$. If the group generated by the support of $\mu$ is non-elementary and contains only loxodromic elements, we show the existence…