Related papers: Finite dimensional point derivations for graph alg…
In this paper, we introduce the concept of inner derivations of low-dimensional Zinbiel algebras and investigate their properties. The primary objective of this study is to develop an algorithm to characterize the inner derivations of any…
This paper deals with $n$-dimensional algebras, over any field, which have only trivial derivation (automorphism) and simple algebras. It is shown that the corresponding sets of algebras are not empty and, in algebraically closed field…
In this paper, we prove that a biderivation of a finite dimensional complex simple Lie algebra without the restriction of skewsymmetric is inner. As an application, the biderivation of a general linear Lie algebra is presented. In…
Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. In this paper we will consider the special case where all division rings are…
Each finite and connected bipartite graph induces a finite collection of non-isomorphic dessins d'enfants, that is, $2$-cell embeddings of it into some closed orientable surface. We describe an algorithm to compute all these dessins…
Given a finite connected bipartite graph, finite-dimensional indecomposable semisimple Leibniz algebras are constructed. Furthermore, any finite-dimensional indecomposable semisimple Leibniz algebra admits a similar construction.
In the present paper 2-local derivations on various algebras of infinite dimensional matrix-valued functions on a compact are considered. It is proved that every 2-local derivation on such algebra is a derivation. Also we explain that the…
We describe the full automorphism group of the directed reduced power graph and the undirected reduced power graph of a finite group. We compute the full automorphism groups of these graphs of several classes of finite groups. Also, we…
In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed graphs by characterizing Morse decompositions, recurrence…
We examine the Maximum Independent Set Problem in an undirected graph. The main result is that this problem can be considered as the solving the same problem in a subclass of the weighted normal twin-orthogonal graphs. The problem is…
Given a directed graph, there exists a universal operator algebra and universal C*-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal…
The present paper is devoted to study 2-local derivations on infinite-dimensional Lie algebras over a field of characteristic zero. We prove that all 2-local derivations on the Witt algebra as well as on the positive Witt algebra are…
We prove that every local derivation on a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero is a derivation. We also give examples of finite-dimensional nilpotent Lie algebras $\mathcal{L}$…
It is well known that central simple algebras are split by suitable finite Galois extensions of their centers. A counterpart of this result was studied by Juan and Magid in the set up of differential matrix algebras, wherein Picard-Vessiot…
The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an…
In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framework, we derive, in particular, a variant of the Birman…
In this paper we verify that the graph forms a complete invariant for Banach algebra isomorphisms of tensor algebras of graphs. For tensor algebras associated with countable directed graphs having no sinks the graph forms an invariant for…
In this paper, we introduce a graph structure, called non-zero component graph on finite dimensional vector spaces. We show that the graph is connected and find its domination number and independence number. We also study the…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
In this paper, we introduce the notion of a finite non-simple directed graph, called an ornated graph and initiate a study on ornated graphs. An ornated graph is a directed graph on $n$ vertices, denoted by $O_n(s_l)$, whose vertices are…