Related papers: Evolution algebras generated by Gibbs measures
In this paper we further develop the theory of one sided shift spaces over infinite alphabets, characterizing one-step shifts as edge shifts of ultragraphs and partially answering a conjecture regarding shifts of finite type (we show that…
In this work we investigate the derivations of $n-$dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero.…
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 define a new notion of an algebraic model structure, in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads, and prove "algebraic" analogs of classical results. Using a modified version…
If A is a finite dimensional nilpotent associative algebra over a finite field k, the set G=1+A of all formal expressions of the form 1+a, where a is an element of A, has a natural group structure, given by (1+a)(1+b)=1+(a+b+ab). A finite…
Let A be an evolution algebra (possibly infinite-dimensional) equipped with a fixed natural basis B, and let E be the associated graph defined by Elduque and Labra. We describe the group of automorphisms of A that are diagonalizable with…
A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…
In earlier work we developed the theory of signatures of hermitian forms over algebras with involution with respect to orderings on the base field of the algebra and obtained in particular that the total signature of a hermitian form is a…
We define a normal graph algebra modeled on algebras used in genetics. Although the algebra does not always determine its graph, it often highlights special features. After developing basic properties of the algebra, we examine those of…
In this work we are going to study the dynamics of the linear automorphisms of a measure convolution algebra over a finite group, $T(\mu)=\nu * \mu$. In order to understand an classify the asymptotic behavior of this dynamical system we…
We generalise gauge theory on a graph so that the gauge group becomes a finite-dimensional ribbon Hopf algebra, the graph becomes a ribbon graph, and gauge-theoretic concepts such as connections, gauge transformations and observables are…
Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature…
We present a method for associating labeled directed graphs to finite-dimensional Lie algebras, thereby enabling rapid identification of key structural algebraic features. To formalize this approach, we introduce the concept of…
In this paper we classify a family of three-dimensional real evolution algebras. We also consider an evolution operator for an evolution algebra and find fixed points of this operator for two and three-dimensional cases. Then we construct…
We investigate subshifts with a general algebraic structure and cellular automata on them, with an emphasis on (order-theoretic) lattices. Our main results concern the characterization of Boolean algebraic subshifts, conditions for…
An enhanced Leibniz algebra is an algebraic struture that arises in the context of particular higher gauge theories describing self-interacting gerbes. It consists of a Leibniz algebra $(\mathbb{V},[ \cdot, \cdot ])$, a bilinear form on…
In this paper, we study modularity in the context of evolution algebras. Although this property has been previously considered, a complete description is still missing in several natural settings. In particular, we obtain a full…
We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…
The main objective of this paper is to study the relationship between a solvable evolution algebra and its subalgebra lattice, emphasizing two of its main properties: distributivity and modularity. First, we will focus on the nilpotent…
Algebraically constructible functions connect real algebra with the topology of algebraic sets. In this survey we present some history, definitions, properties, and algebraic characterizations of algebraically constructible functions, and a…