Related papers: Bounded Generation for $SL_n(\Lambda)$
In this research we continue our previous investigation of wreath product normal structure \cite{SkuESL}. We generalize the group of unimodular matrices \cite{Amit} and find its structure. For this goal we propose one extension of the…
Constrained generative modeling is fundamental to applications such as robotic control and autonomous driving, where models must respect physical laws and safety-critical constraints. In real-world settings, these constraints rarely take…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, inductive limit group, Zariski topology and the dimension of the…
It is proven that the partition function of 3-dimensional simplicial gravity has an exponential upper bound with the following assumption: any three dimensional sphere $S^3$ is constructed by repeated identification of neighboring links and…
This note concerns bounded derivations on maximal triangular operator algebras on a Hilbert space. Given any bounded derivation $\delta$ on a maximal triangular algebra whose invariant lattice is continuous at 1, an operator which is shown…
The generators of the algebra $gl_{n+1}$ in a form of differential operators of the first order acting on ${\bf R}^n$ with matrix coefficients are explicitly written. The algebraic Hamiltonians for a matrix generalization of $3-$body…
We give a new non-trivial upper bound for the Selberg integral of the three-divisor function $d_3(n)$. Our method applies our recent conjecture together with Laporta, for the modified Selberg integral of $d_3(n)$, and a kind of modified…
Suppose $\Lambda$ is a special biserial algebra over an algebraically closed field. Schr\"oer showed that if $\Lambda$ is domestic then the radical of the category of finitely generated (left) $\Lambda$-modules is nilpotent, and the least…
Our first result provides a new characterization of Auslander algebras using a property of hereditary torsion pairs. The second result shows an Auslander algebra $\Lambda$ is left or right glued if and only if $\Lambda$ is…
A subset $\left\{x_{1},x_{2},\hdots,x_{d}\right\}$ of a group $G$ \emph{invariably generates} $G$ if $\left\{x_{1}^{g_{1}},x_{2}^{g_{2}},\hdots,x_{d}^{g_{d}}\right\}$ generates $G$ for every $d$-tuple $(g_{1},g_{2}\hdots,g_{d})\in G^{d}$.…
We study bounded width algebras which are minimal in the sense that every proper reduct does not have bounded width. We show that minimal bounded width algebras can be arranged into a pseudovariety with one basic ternary operation. We…
We prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.
In a permutation sequence built by means of sub permutations the transition between successive permutations are subject to a set of n(n - 1)/2 rules that group into n - 1 matrices with a high degree of regularity. By means of these rules…
In this paper we study algebraic and asymptotic properties of generating sets of algebras over orders in number fields. Let $A$ be an associative algebra over an order $R$ in an algebraic number field. We assume that $A$ is a free…
Let $\lambda$ be a partition of an integer $n$ and ${\mathbb F}_q$ be a finite field of order $q$. Let $P_\lambda(q)$ be the number of strictly upper triangular $n\times n$ matrices of the Jordan type $\lambda$. It is known that the…
We explore some properties of wide subcategories of the category mod$\,(\Lambda)$ of finitely generated left $\Lambda$-modules, for some artin algebra $\Lambda.$ In particular we look at wide finitely generated subcategories and give a…
We give the generating function for the index of integer lattice points, relative to a finite order ideal. The index is an important concept in the theory of border bases, an alternative to Gr\"obner bases. Equivalently, we explicitly solve…
We consider Euclidean lattices spanned by images of algebraic conjugates of an algebraic number under Minkowski embedding, investigating their rank, properties of their automorphism groups and sets of minimal vectors. We are especially…
This paper is concerned with the diameter of certain word norms on S-arithmetic split Chevalley groups. Such groups are well known to be boundedly generated by root elements. We prove that word metrics given by conjugacy classes on…