Related papers: Evolution algebras and graphs
We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the…
A general random graph evolution mechanism is defined. The evolution is a combination of the preferential attachment model and the interaction of N vertices (N>=3). A vertex in the graph is characterized by its degree and its weight. The…
We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.
Inspired by Franks' classification of irreducible shifts of finite type we provide a short list of allowed moves on graphs that preserves the stable isomorphism class of the associated C*-algebras. We show that if two graphs have stably…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
We construct non-isogenous simple ordinary abelian varieties over an algebraic closure of a finite field with isomorphic endomorphism algebras.
Given a simple undirected graph, one can construct from it a $c$-step nilpotent Lie algebra for every $c \geq 2$ and over any field $K$, in particular also over the real and complex numbers. These Lie algebras form an important class of…
Let $G$ be a finite non-abelian simple group, $C$ a non-identity conjugacy class of $G$, and $\Gamma_C$ the Cayley graph of $G$ based on $C \cup C^{-1}$. Our main result shows that in any such graph, there is an involution at bounded…
An A-infinity algebra is a generalization of a associative algebra, and an L-infinity algebra is a generalization of a Lie algebra. In this paper, we show that an L-infinity algebra with an invariant inner product determines a cycle in the…
This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length $k$ in a graph with $N\geq k$ edges and no loops. Our proof relies on a construction of a number of terminating algorithms that…
The deformations of an infinite dimensional algebra may be controlled not just by its own cohomology but by that of an associated diagram of algebras, since an infinite dimensional algebra may be absolutely rigid in the classical…
The notion of ends in an infinite graph $G$ might be modified if we consider them as equivalence classes of infinitely edge-connected rays, rather than equivalence classes of infinitely (vertex-)connected ones. This alternative definition…
We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra $\A$ in two cases: when $\A$ is of geometric type and when $\A$ is arbitrary and its exchange matrix is nondegenerate. In the second case we also…
An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist…
Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. D\'enes proved that the permutation is a full cyclic permutation…
We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the…
Results describing Lie ideals and maximal finite-codimensional Lie subalgebras of the Lie algebras associated with Lie algebroids with non-singular anchor maps are presented. It is also proved that every isomorphism of such Lie algebras…
We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…
Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of…
We generalize the enhanced power graph by replacing elements with classes under automorphisms. We show that the connectivity and diameter of this graph is similar to that of the enhanced power graph. We consider the universal vertices of…