Related papers: Finitely Generated Nil but Not Nilpotent Evolution…
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…
We prove that the growth rate of an endomorphism of a finitely generated nilpotent group equals to the growth rate of induced endomorphism on its abelinization, generalizing the corresponding result for an automorphism in [14]. We also…
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…
Evolution algebras are non-associative algebras that describe non-Mendelian hereditary processes and have connections with many other areas. In this paper we obtain necessary and sufficient conditions for a given algebra $A$ to be an…
A nilpotent quotient algorithm for finitely presented Lie rings over Z (LieNQ) is described. The paper studies graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented,…
We prove that every nilpotent commutative algebra can be embedded into a pre-commutative (Zinbiel) algebra with respect to the anti-commutator operation. For finite-dimensional algebras, the nilpotency condition is necessary for a…
The class of associative trialgebras, also known as triassociative algebras, is characterized by three multiplications and eleven relations that generalize associativity. In the current paper, we present a study of nilpotent triassociative…
This paper investigates the finite generation of cluster automorphism groups. By applying the pseudo $\mathbb{N}$-grading introduced in our previous work, we establish a sufficient condition for a cluster automorphism group to be finitely…
We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the basic properties of finite algebras in these varieties such…
Ufnarovski remarked in 1990 that it is unknown whether any finitely presented associative algebra of linear growth is automaton, that is, whether the set of normal words in the algebra form a regular language. If the algebra is graded, then…
Let $\Gamma$ be a finitely generated nilpotent group and let G be a complex reductive algebraic group. The representation variety $\mathrm{Hom}(\Gamma,G)$ and the character variety $\mathrm{Hom}(\Gamma,G)//G$ each carry a natural topology,…
Let $\Gamma$ and $\Lambda$ be artin algebras such that $\Gamma$ is a split-by-nilpotent extension of $\Lambda$ by a two sided ideal $I$ of $\Gamma.$ Consider the so-called change of rings functors $G:={}_\Gamma\Gamma_\Lambda\otimes_\Lambda…
An automorphism defined on an evolution algebra can provide both a finite number and an infinite number of evolution operators on it. This question is dealt with in the paper, as well as others more related to the evolution operators of…
We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, in the nilpotent case. It turns out that in the o-minimal context, like for finite groups, nilpotency is equivalent to…
The nilpotent graph of a group $G$ is the simple and undirected graph whose vertices are the elements of $G$ and two distinct vertices are adjacent if they generate a nilpotent subgroup of $G$. Here we discuss some topological properties of…
For some monoids, we give a method of composing invertibility preserving maps associated to "partial involutions." Also, we define the notion of "determinants for finite dimensional algebras over a field." As examples, we give invertibility…
Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to…
We prove that if an involution in a ring is the sum of an idempotent and a nilpotent then the idempotent in this decomposition must be 1. As a consequence, we completely characterize weakly nil-clean rings introduced recently in [Breaz,…
A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…
In 1964, Golod and Shafarevich found that, provided that the number of relations of each degree satisfy some bounds, there exist infinitely dimensional algebras satisfying the relations. These algebras are called Golod-Shafarevich algebras.…