Related papers: Growth estimates for discrete quantum groups

Let $m_n(G)$ denote the number of maximal subgroups of $G$ of index $n$. An upper bound is given for the degree of maximal subgroup growth of all polycyclic metabelian groups $G$ (i.e., for $\limsup \frac{\log m_n(G)}{\log n}$, the degree…

We show that every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) has linear growth. This implies that the the corresponding semigroup algebra is a PI algebra.

We construct the HNN extension of discrete quantum groups, we study their representation theory and we show that an HNN extension of amenable discrete quantum groups is K-amenable.

In this paper we aim to establish some results depending on the comparative growth properties of composite transcendental entire or meromorphic functions and some special type of differential polynomials generated by one of the factors on…

We study completions of the group algebra of a finitely generated group and relate nuclearity of such a completion to growth properties of the group. This extends previous work of Jolissaint on nuclearity of rapidly decreasing functions on…

The paper considers a general concept of dichotomy with different growth rates for linear discrete-time systems in Banach spaces. Characterizations in terms of Lyapunov type sequences of norms are given. The approach is illustrated by…

We study the growth of the central polynomials for the algebras $G$ and $M_k(F)$, the infinite dimensional Grassmann algebra and the $k\times k$ matrices over a field $F$ of characteristic zero. In particular it follows that $M_k(F)$…

Let $K = \mathbb{Q}(\sqrt{-3})$ or $\mathbb{Q}(\sqrt{-1})$ and let $C_n$ denote the cyclic group of order $n$. We study how the torsion part of an elliptic curve over $K$ grows in a quadratic extension of $K$. In the case $E(K)[2] \approx…

We prove that if $\Gamma$ is a group of polynomial growth then each delocalized cyclic cocycle on the group algebra has a representative of polynomial growth. For each delocalized cocyle we thus define a higher analogue of Lott's…

Wave functions of bounded quantum systems with time-independent potentials, being almost periodic functions, cannot have time asymptotics as in classical chaos. However, bounded quantum systems with time-dependent interactions, as used in…

In this paper we study the problem of approximation of the $L^2$-topological invariants by their finite dimensional analogues. We obtain generalizations of the theorem of L\"uck, dealing with towers of finitely sheeted normal coverings. We…

We study the rapid decay property and polynomial growth for duals of bicrossed products coming from a matched pair of a discrete group and a compact group

We study about order of growth and hyper order of growth of non trivial solutions of second order linear differential equations, having restrictions in the coefficients. These restrictions involve notions of Yang's inequality, Borel…

We resolve two open problems on Kronecker coefficients $g(\lambda,\mu,\nu)$ of the symmetric group. First, we prove that for partitions $\lambda,\mu,\nu$ with fixed Durfee square size, the Kronecker coefficients grow at most polynomially.…

We prove that the so called Grigorchuk-Maki group of intermadiate growth can be seen as a group of $C^1$ diffeomorphisms of the interval. On the other hand, we prove that every group of $C^{1+\alpha}$ diffeomorphisms of the interval having…

By now, we have a product theorem in every finite simple group $G$ of Lie type, with the strength of the bound depending only in the rank of $G$. Such theorems have numerous consequences: bounds on the diameters of Cayley graphs, spectral…

Babai's conjecture states that, for any finite simple non-abelian group $G$, the diameter of $G$ is bounded by $(\log|G|)^{C}$ for some absolute constant $C$. We prove that, for any untwisted classical group $G$ of rank $r$ defined over a…

We calculate explicit estimates for the dimension of trajectories satisfying a certain growth bound. We generalize the classic results of Kurzweil by considering nonlinear nonautonomous and uniformly compact dynamical systems on normed…

We initiate the study of the ''algebraic growth'' of groups of automorphisms and birational transformations of algebraic varieties. Our main result concerns $\text{Bir}(\mathbb{P}^2)$, the Cremona group in $2$ variables. This group is the…

We study prime algebras of quadratic growth. Our first result is that if $A$ is a prime monomial algebra of quadratic growth then $A$ has finitely many prime ideals $P$ such that $A/P$ has GK dimension one. This shows that prime monomial…