Related papers: Algebraic characterisations of path algebras
We explore graph theoretical properties of minimal prime graphs of finite solvable groups. In finite group theory studying the prime graph of a group has been an important topic for the past almost half century. Recently prime graphs of…
We provide a characterization of graded von Neumann regular rings involving the recently introduced class of nearly epsilon-strongly graded rings. As our main application, we generalize Hazrat's result that Leavitt path algebras over fields…
Path and boundary-path groupoids of finitely aligned higher-rank graphs are often constructed using either filters or graph morphisms. We generalise the graph morphism approach to finitely aligned P-graphs where (Q, P) is a weakly…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Evolution algebras are non-associative algebras inspired from biological phenomena, with applications to or connections with different mathematical fields. There are two natural ways to define an evolution algebra associated to a given…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
We study the connection between two combinatorial notions associated to a quiver: the quiver algebra and the path coalgebra. We show that the quiver coalgebra can be recovered from the quiver algebra as a certain type of finite dual, and we…
We show that finite dimensional half-quantum groups at roots of unity corresponding to simple Lie algebras having symmetric Cartan matrix are of wild representation type, except for sl_2. Moreover, the underlying associative algebra is…
While every matrix algebra over a field $K$ can be realized as a Leavitt path algebra, this is not the case for every graded matrix algebra over a graded field. We provide a complete description of graded matrix algebras over a field,…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
In this paper we give some sufficient and some necessary conditions for an \'etale groupoid algebra to be a prime ring. As an application we recover the known primeness results for inverse semigroup algebras and Leavitt path algebras. It…
Let $G$ be a complete graph with $n+1$ vertices. In a recent paper of the authors, it is shown that the path trees of the graph play a special role in the structure of the truncated powers and partition functions that are associated with…
We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…
We first establish several general properties of modality of algebraic group actions. In particular, we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we…
Given any arbitrary semi-algebraic set $X$, any two points in $X$ may be joined by a piecewise $C^2$ path $\gamma$ of shortest length. Suppose $\mathcal{A}$ is a semi-algebraic stratification of $X$ such that each component of $\gamma \cap…
Directed graphs have long been used to gain understanding of the structure of semigroups, and recently the structure of directed graph semigroups has been investigated resulting in a characterization theorem and an analog of Fruct's…
We introduce the concept of "irrational paths" for a given subshift and use it to characterize all minimal left ideals in the associated unital subshift algebra. Consequently, we characterize the socle as the sum of the ideals generated by…
Given an arbitrary graph, we describe the center of its Leavitt path algebra over a commutative unital ring. Our proof uses the Steinberg algebra model of the Leavitt path algebra. A key ingredient is a characterization of compact open…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…
Let $G$ be a group. We define the coprime graph of subgroups of $G$, denoted by $\mathcal P(G)$, is a graph whose vertex set is the set of all proper subgroups of $G$, and two distinct vertices are adjacent if and only if the order of the…